sharman decides to travel 100 km

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Quantitative Aptitude (QA) Solved MCQ | CAT | Part 5

Cat, cmat, xat, mat, gmat, iift, snap, nmat by gmac, atma, ibsat, ts icet, ap icet, jemat, mah mba cet, b-mat, niper jee mba, cusat cat, tissnet, micat, kiitee management, upes met, karnataka pgcet, kmat, tancet, irmasat solved practice questions (qa) - part 5.

Chapter - Alligations Difficulty Level of Questions - 1 (Out of 3)

Q.1. 800 students took the cat exam in delhi. 50% of the boys and 90% of the girls cleared the cut off in the examination. if the total percentage of qualifying students is 60%, how many girls appeared in the examination.

Q.2. Raman steals four gallons of liquid soap kept in a train compartment's bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again and fills it with water. When the liquid soap is checked at a station it is found that the ratio of the liquid soap now left in the container to that of the water in it is 36: 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?

Q.3. In what ratio should water be mixed with soda costing ₹ 12 per litre so as to make a profit of 50% by selling the diluted liquid at ₹ 15 per litre?

Q.4. A sum of ₹ 4 is made up of 20 coins that are either 10 paise coins or 60 paise coins. Find out how many 10 paise coins are there in the total amount.

Q.5. Pinku a dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 25%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available.

Q.6. A bag contains a total of 105 coins of ₹ 1, 50 p and 25 p denominations. Find the total number of coins of ₹ 1 if there are a total of 50.5 rupees in the bag and it is known that the number of 25 paise coins is 133.33% more than the number of 1 rupee coins.

Q.7. Two buckets of equal capacity are full of a mixture of milk and water. In the first, the ratio of milk to water is 1:7 and in the second it is 3:8. Now both the mixtures are mixed in a bigger container. What is the resulting ratio of milk to water?

Q.8. Two vessels contain spirit and water mixed respectively in the ratio of 1:4 and 4:1. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1:3.

Q.9. In the Delhi zoo, there are lions and there are hens If the heads are counted, there are 180, while the legs are 448. What will be the number of lions in the zoo?

Q.10. Sharman decides to travel 100 kilometres in 8 hours partly by foot and partly on a bicycle, his speed on foot being 10 km/h and that on a bicycle being 20 km/h, what distance would he travel on foot?

Questions Courtesy:  How to prepare for Quantitative Aptitude for CAT by Arun Sharma

Books i recommend for quantitative aptitude:, 1. how to prepare for quantitative aptitude for cat by arun sharma, 2. ace quantitative aptitude for banking and insurance, 3. quantitative aptitude quantum cat by sarvesh k verma, 4. quantitative aptitude for competitive examinations by r.s. aggarwal, 5. best 4000 smart practice questions for banking by s. chand experts, about the author, post a comment.

If a man decides to travel 80 kilometres in 8 hours partly by foot and partly on a bicycle, his speed on foot being 8 km/h and that on bicycle being 16 km/h, what distance would he travel on foot?

The correct option is c 48 km average speed = 80 8 = 10 k m / h hence, by alligation ratio of time travelled by foot to that on bicycle = 6 : 2. ∴ distance travelled by foot = 8 × 6 = 48 k m alternate approach: solve using options. if he travels 48 km on foot he would take 6 hours on foot. also. in this case, he would travel 32 km on bicycle at 16 km/h - which would take him 2 hours. thus a total of 8 hours. option (c) satisfies the conditions of the question..

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Algebra Topics  - Distance Word Problems

Algebra topics  -, distance word problems, algebra topics distance word problems.

Algebra Topics: Distance Word Problems

Lesson 10: distance word problems.

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What are distance word problems?

Distance word problems are a common type of algebra word problems. They involve a scenario in which you need to figure out how fast , how far , or how long one or more objects have traveled. These are often called train problems because one of the most famous types of distance problems involves finding out when two trains heading toward each other cross paths.

In this lesson, you'll learn how to solve train problems and a few other common types of distance problems. But first, let's look at some basic principles that apply to any distance problem.

The basics of distance problems

There are three basic aspects to movement and travel: distance , rate , and time . To understand the difference among these, think about the last time you drove somewhere.

The distance is how far you traveled. The rate is how fast you traveled. The time is how long the trip took.

The relationship among these things can be described by this formula:

distance = rate x time d = rt

In other words, the distance you drove is equal to the rate at which you drove times the amount of time you drove. For an example of how this would work in real life, just imagine your last trip was like this:

• You drove 25 miles—that's the distance .
• You drove an average of 50 mph—that's the rate .
• The drive took you 30 minutes, or 0 .5 hours—that's the time .

According to the formula, if we multiply the rate and time , the product should be our distance.

And it is! We drove 50 mph for 0.5 hours—and 50 ⋅ 0.5 equals 25 , which is our distance.

What if we drove 60 mph instead of 50? How far could we drive in 30 minutes? We could use the same formula to figure this out.

60 ⋅ 0.5 is 30, so our distance would be 30 miles.

Solving distance problems

When you solve any distance problem, you'll have to do what we just did—use the formula to find distance , rate , or time . Let's try another simple problem.

On his day off, Lee took a trip to the zoo. He drove an average speed of 65 mph, and it took him two-and-a-half hours to get from his house to the zoo. How far is the zoo from his house?

First, we should identify the information we know. Remember, we're looking for any information about distance, rate, or time. According to the problem:

• The rate is 65 mph.
• The time is two-and-a-half hours, or 2.5 hours.
• The distance is unknown—it's what we're trying to find.

You could picture Lee's trip with a diagram like this:

This diagram is a start to understanding this problem, but we still have to figure out what to do with the numbers for distance , rate , and time . To keep track of the information in the problem, we'll set up a table. (This might seem excessive now, but it's a good habit for even simple problems and can make solving complicated problems much easier.) Here's what our table looks like:

We can put this information into our formula: distance = rate ⋅ time .

We can use the distance = rate ⋅ time formula to find the distance Lee traveled.

The formula d = rt looks like this when we plug in the numbers from the problem. The unknown distance is represented with the variable d .

d = 65 ⋅ 2.5

To find d , all we have to do is multiply 65 and 2.5. 65 ⋅ 2.5 equals 162.5 .

We have an answer to our problem: d = 162.5. In other words, the distance Lee drove from his house to the zoo is 162.5 miles.

Be careful to use the same units of measurement for rate and time. It's possible to multiply 65 miles per hour by 2.5 hours because they use the same unit: an hour . However, what if the time had been written in a different unit, like in minutes ? In that case, you'd have to convert the time into hours so it would use the same unit as the rate.

Solving for rate and time

In the problem we just solved we calculated for distance , but you can use the d = rt formula to solve for rate and time too. For example, take a look at this problem:

After work, Janae walked in her neighborhood for a half hour. She walked a mile-and-a-half total. What was her average speed in miles per hour?

We can picture Janae's walk as something like this:

And we can set up the information from the problem we know like this:

The table is repeating the facts we already know from the problem. Janae walked one-and-a-half miles or 1.5 miles in a half hour, or 0.5 hours.

As always, we start with our formula. Next, we'll fill in the formula with the information from our table.

The rate is represented by r because we don't yet know how fast Janae was walking. Since we're solving for r , we'll have to get it alone on one side of the equation.

1.5 = r ⋅ 0.5

Our equation calls for r to be multiplied by 0.5, so we can get r alone on one side of the equation by dividing both sides by 0.5: 1.5 / 0.5 = 3 .

r = 3 , so 3 is the answer to our problem. Janae walked 3 miles per hour.

In the problems on this page, we solved for distance and rate of travel, but you can also use the travel equation to solve for time . You can even use it to solve certain problems where you're trying to figure out the distance, rate, or time of two or more moving objects. We'll look at problems like this on the next few pages.

Two-part and round-trip problems

Do you know how to solve this problem?

Bill took a trip to see a friend. His friend lives 225 miles away. He drove in town at an average of 30 mph, then he drove on the interstate at an average of 70 mph. The trip took three-and-a-half hours total. How far did Bill drive on the interstate?

This problem is a classic two-part trip problem because it's asking you to find information about one part of a two-part trip. This problem might seem complicated, but don't be intimidated!

You can solve it using the same tools we used to solve the simpler problems on the first page:

• The travel equation d = rt
• A table to keep track of important information

Let's start with the table . Take another look at the problem. This time, the information relating to distance , rate , and time has been underlined.

Bill took a trip to see a friend. His friend lives 225 miles away. He drove in town at an average of 30 mph , then he drove on the interstate at an average of 70 mph . The trip took three-and-a-half hours total. How far did Bill drive on the interstate?

If you tried to fill in the table the way we did on the last page, you might have noticed a problem: There's too much information. For instance, the problem contains two rates— 30 mph and 70 mph . To include all of this information, let's create a table with an extra row. The top row of numbers and variables will be labeled in town , and the bottom row will be labeled interstate .

We filled in the rates, but what about the distance and time ? If you look back at the problem, you'll see that these are the total figures, meaning they include both the time in town and on the interstate. So the total distance is 225 . This means this is true:

Interstate distance + in-town distance = Total distance

Together, the interstate distance and in-town distance are equal to the total distance. See?

In any case, we're trying to find out how far Bill drove on the interstate , so let's represent this number with d . If the interstate distance is d , it means the in-town distance is a number that equals the total, 225 , when added to d . In other words, it's equal to 225 - d .

We can fill in our chart like this:

We can use the same technique to fill in the time column. The total time is 3.5 hours . If we say the time on the interstate is t , then the remaining time in town is equal to 3.5 - t . We can fill in the rest of our chart.

Now we can work on solving the problem. The main difference between the problems on the first page and this problem is that this problem involves two equations. Here's the one for in-town travel :

225 - d = 30 ⋅ (3.5 - t)

And here's the one for interstate travel :

If you tried to solve either of these on its own, you might have found it impossible: since each equation contains two unknown variables, they can't be solved on their own. Try for yourself. If you work either equation on its own, you won't be able to find a numerical value for d . In order to find the value of d , we'll also have to know the value of t .

We can find the value of t in both problems by combining them. Let's take another look at our travel equation for interstate travel.

While we don't know the numerical value of d , this equation does tell us that d is equal to 70 t .

Since 70 t and d are equal , we can replace d with 70 t . Substituting 70 t for d in our equation for interstate travel won't help us find the value of t —all it tells us is that 70 t is equal to itself, which we already knew.

But what about our other equation, the one for in-town travel?

When we replace the d in that equation with 70 t , the equation suddenly gets much easier to solve.

225 - 70t = 30 ⋅ (3.5 - t)

Our new equation might look more complicated, but it's actually something we can solve. This is because it only has one variable: t . Once we find t , we can use it to calculate the value of d —and find the answer to our problem.

To simplify this equation and find the value of t , we'll have to get the t alone on one side of the equals sign. We'll also have to simplify the right side as much as possible.

Let's start with the right side: 30 times (3.5 - t ) is 105 - 30 t .

225 - 70t = 105 - 30t

Next, let's cancel out the 225 next to 70 t . To do this, we'll subtract 225 from both sides. On the right side, it means subtracting 225 from 105 . 105 - 225 is -120 .

- 70t = -120 - 30t

Our next step is to group like terms—remember, our eventual goal is to have t on the left side of the equals sign and a number on the right . We'll cancel out the -30 t on the right side by adding 30 t to both sides. On the right side, we'll add it to -70 t . -70 t + 30 t is -40 t .

- 40t = -120

Finally, to get t on its own, we'll divide each side by its coefficient: -40. -120 / - 40 is 3 .

So t is equal to 3 . In other words, the time Bill traveled on the interstate is equal to 3 hours . Remember, we're ultimately trying to find the distanc e Bill traveled on the interstate. Let's look at the interstate row of our chart again and see if we have enough information to find out.

It looks like we do. Now that we're only missing one variable, we should be able to find its value pretty quickly.

To find the distance, we'll use the travel formula distance = rate ⋅ time .

We now know that Bill traveled on the interstate for 3 hours at 70 mph , so we can fill in this information.

d = 3 ⋅ 70

Finally, we finished simplifying the right side of the equation. 3 ⋅ 70 is 210 .

So d = 210 . We have the answer to our problem! The distance is 210 . In other words, Bill drove 210 miles on the interstate.

Solving a round-trip problem

It might have seemed like it took a long time to solve the first problem. The more practice you get with these problems, the quicker they'll go. Let's try a similar problem. This one is called a round-trip problem because it describes a round trip—a trip that includes a return journey. Even though the trip described in this problem is slightly different from the one in our first problem, you should be able to solve it the same way. Let's take a look:

Eva drove to work at an average speed of 36 mph. On the way home, she hit traffic and only drove an average of 27 mph. Her total time in the car was 1 hour and 45 minutes, or 1.75 hours. How far does Eva live from work?

If you're having trouble understanding this problem, you might want to visualize Eva's commute like this:

As always, let's start by filling in a table with the important information. We'll make a row with information about her trip to work and from work .

1.75 - t to describe the trip from work. (Remember, the total travel time is 1.75 hours , so the time to work and from work should equal 1.75 .)

From our table, we can write two equations:

• The trip to work can be represented as d = 36 t .
• The trip from work can be represented as d = 27 (1.75 - t ) .

In both equations, d represents the total distance. From the diagram, you can see that these two equations are equal to each other—after all, Eva drives the same distance to and from work .

Just like with the last problem we solved, we can solve this one by combining the two equations.

We'll start with our equation for the trip from work .

d = 27 (1.75 - t)

Next, we'll substitute in the value of d from our to work equation, d = 36 t . Since the value of d is 36 t , we can replace any occurrence of d with 36 t .

36t = 27 (1.75 - t)

Now, let's simplify the right side. 27 ⋅(1.75 - t ) is 47.25 .

36t = 47.25 - 27t

Next, we'll cancel out -27 t by adding 27 t to both sides of the equation. 36 t + 27 t is 63 t .

63t = 47.25

Finally, we can get t on its own by dividing both sides by its coefficient: 63 . 47.25 / 63 is .75 .

t is equal to .75 . In other words, the time it took Eva to drive to work is .75 hours . Now that we know the value of t , we'll be able to can find the distance to Eva's work.

If you guessed that we were going to use the travel equation again, you were right. We now know the value of two out of the three variables, which means we know enough to solve our problem.

First, let's fill in the values we know. We'll work with the numbers for the trip to work . We already knew the rate : 36 . And we just learned the time : .75 .

d = 36 ⋅ .75

Now all we have to do is simplify the equation: 36 ⋅ .75 = 27 .

d is equal to 27 . In other words, the distance to Eva's work is 27 miles . Our problem is solved.

Intersecting distance problems

An intersecting distance problem is one where two things are moving toward each other. Here's a typical problem:

Pawnee and Springfield are 420 miles apart. A train leaves Pawnee heading to Springfield at the same time a train leaves Springfield heading to Pawnee. One train is moving at a speed of 45 mph, and the other is moving 60 mph. How long will they travel before they meet?

This problem is asking you to calculate how long it will take these two trains moving toward each other to cross paths. This might seem confusing at first. Even though it's a real-world situation, it can be difficult to imagine distance and motion abstractly. This diagram might help you get a sense of what this situation looks like:

If you're still confused, don't worry! You can solve this problem the same way you solved the two-part problems on the last page. You'll just need a chart and the travel formula .

Pawnee and Springfield are 420 miles apart. A train leaves Pawnee heading toward Springfield at the same time a train leaves Springfield heading toward Pawnee. One train is moving at a speed of 45 mph , and the other is moving 60 mph . How long will they travel before they meet?

Let's start by filling in our chart. Here's the problem again, this time with the important information underlined. We can start by filling in the most obvious information: rate . The problem gives us the speed of each train. We'll label them fast train and slow train . The fast train goes 60 mph . The slow train goes only 45 mph .

We can also put this information into a table:

We don't know the distance each train travels to meet the other yet—we just know the total distance. In order to meet, the trains will cover a combined distance equal to the total distance. As you can see in this diagram, this is true no matter how far each train travels.

This means that—just like last time—we'll represent the distance of one with d and the distance of the other with the total minus d. So the distance for the fast train will be d , and the distance for the slow train will be 420 - d .

Because we're looking for the time both trains travel before they meet, the time will be the same for both trains. We can represent it with t .

The table gives us two equations: d = 60 t and 420 - d = 45 t . Just like we did with the two-part problems, we can combine these two equations.

The equation for the fast train isn't solvable on its own, but it does tell us that d is equal to 60 t .

The other equation, which describes the slow train, can't be solved alone either. However, we can replace the d with its value from the first equation.

420 - d = 45t

Because we know that d is equal to 60 t , we can replace the d in this equation with 60 t . Now we have an equation we can solve.

420 - 60t = 45t

To solve this equation, we'll need to get t and its coefficients on one side of the equals sign and any other numbers on the other. We can start by canceling out the -60 t on the left by adding 60 t to both sides. 45 t + 60 t is 105 t .

Now we just need to get rid of the coefficient next to t . We can do this by dividing both sides by 105 . 420 / 105 is 4 .

t = 4 . In other words, the time it takes the trains to meet is 4 hours . Our problem is solved!

If you want to be sure of your answer, you can check it by using the distance equation with t equal to 4 . For our fast train, the equation would be d = 60 ⋅ 4 . 60 ⋅ 4 is 240 , so the distance our fast train traveled would be 240 miles. For our slow train, the equation would be d = 45 ⋅ 4 . 45 ⋅ 4 is 180 , so the distance traveled by the slow train is 180 miles . Remember how we said the distance the slow train and fast train travel should equal the total distance? 240 miles + 180 miles equals 420 miles , which is the total distance from our problem. Our answer is correct.

Practice problem 1

Here's another intersecting distance problem. It's similar to the one we just solved. See if you can solve it on your own. When you're finished, scroll down to see the answer and an explanation.

Jon and Dani live 270 miles apart. One day, they decided to drive toward each other and hang out wherever they met. Jon drove an average of 65 mph, and Dani drove an average of 70 mph. How long did they drive before they met up?

Problem 1 answer

Here's practice problem 1:

Jon and Dani live 270 miles apart. One day, they decided to drive toward each other and hang out wherever they met. Jon drove an average of 65 mph, and Dani drove 70 mph. How long did they drive before they met up?

Answer: 2 hours .

Let's solve this problem like we solved the others. First, try making the chart. It should look like this:

Here's how we filled in the chart:

• Distance: Together, Dani and Jon will have covered the total distance between them by the time they meet up. That's 270 . Jon's distance is represented by d , so Dani's distance is 270 - d .
• Rate: The problem tells us Dani and Jon's speeds. Dani drives 65 mph , and Jon drives 70 mph .
• Time: Because Jon and Dani drive the same amount of time before they meet up, both of their travel times are represented by t .

Now we have two equations. The equation for Jon's travel is d = 65 t . The equation for Dani's travel is 270 - d = 70 t . To solve this problem, we'll need to combine them.

The equation for Jon tells us that d is equal to 65 t . This means we can combine the two equations by replacing the d in Dani's equation with 65 t .

270 - 65t = 70t

Let's get t on one side of the equation and a number on the other. The first step to doing this is to get rid of -65 t on the left side. We'll cancel it out by adding 65 t to both sides: 70 t + 65 t is 135 t .

All that's left to do is to get rid of the 135 next to the t . We can do this by dividing both sides by 135 : 270 / 135 is 2 .

That's it. t is equal to 2 . We have the answer to our problem: Dani and Jon drove 2 hours before they met up.

Overtaking distance problems

The final type of distance problem we'll discuss in this lesson is a problem in which one moving object overtakes —or passes —another. Here's a typical overtaking problem:

The Hill family and the Platter family are going on a road trip. The Hills left 3 hours before the Platters, but the Platters drive an average of 15 mph faster. If it takes the Platter family 13 hours to catch up with the Hill family, how fast are the Hills driving?

You can picture the moment the Platter family left for the road trip a little like this:

The problem tells us that the Platter family will catch up with the Hill family in 13 hours and asks us to use this information to find the Hill family's rate . Like some of the other problems we've solved in this lesson, it might not seem like we have enough information to solve this problem—but we do. Let's start making our chart. The distance can be d for both the Hills and the Platters—when the Platters catch up with the Hills, both families will have driven the exact same distance.

Filling in the rate and time will require a little more thought. We don't know the rate for either family—remember, that's what we're trying to find out. However, we do know that the Platters drove 15 mph faster than the Hills. This means if the Hill family's rate is r , the Platter family's rate would be r + 15 .

Now all that's left is the time. We know it took the Platters 13 hours to catch up with the Hills. However, remember that the Hills left 3 hours earlier than the Platters—which means when the Platters caught up, they'd been driving 3 hours more than the Platters. 13 + 3 is 16 , so we know the Hills had been driving 16 hours by the time the Platters caught up with them.

Our chart gives us two equations. The Hill family's trip can be described by d = r ⋅ 16 . The equation for the Platter family's trip is d = ( r + 15) ⋅ 13 . Just like with our other problems, we can combine these equations by replacing a variable in one of them.

The Hill family equation already has the value of d equal to r ⋅ 16. So we'll replace the d in the Platter equation with r ⋅ 16 . This way, it will be an equation we can solve.

r ⋅ 16 = (r + 15) ⋅ 13

First, let's simplify the right side: r ⋅ 16 is 16 r .

16r = (r + 15) ⋅ 13

Next, we'll simplify the right side and multiply ( r + 15) by 13 .

16r = 13r + 195

We can get both r and their coefficients on the left side by subtracting 13 r from 16 r : 16 r - 13 r is 3 r .

Now all that's left to do is get rid of the 3 next to the r . To do this, we'll divide both sides by 3: 195 / 3 is 65 .

So there's our answer: r = 65. The Hill family drove an average of 65 mph .

You can solve any overtaking problem the same way we solved this one. Just remember to pay special attention when you're setting up your chart. Just like the Hill family did in this problem, the person or vehicle who started moving first will always have a greater travel time.

Practice problem 2

Try solving this problem. It's similar to the problem we just solved. When you're finished, scroll down to see the answer and an explanation.

A train moving 60 mph leaves the station at noon. An hour later, a train moving 80 mph leaves heading the same direction on a parallel track. What time does the second train catch up to the first?

Problem 2 answer

Here's practice problem 2:

Answer: 4 p.m.

To solve this problem, start by making a chart. Here's how it should look:

Here's an explanation of the chart:

• Distance: Both trains will have traveled the same distance by the time the fast train catches up with the slow one, so the distance for both is d .
• Rate: The problem tells us how fast each train was going. The fast train has a rate of 80 mph , and the slow train has a rate of 60 mph .
• Time: We'll use t to represent the fast train's travel time before it catches up. Because the slow train started an hour before the fast one, it will have been traveling one hour more by the time the fast train catches up. It's t + 1 .

Now we have two equations. The equation for the fast train is d = 80 t . The equation for the slow train is d = 60 ( t + 1) . To solve this problem, we'll need to combine the equations.

The equation for the fast train says d is equal to 80 t . This means we can combine the two equations by replacing the d in the slow train's equation with 80 t .

80t = 60 (t + 1)

First, let's simplify the right side of the equation: 60 ⋅ ( t + 1) is 60 t + 60 .

80t = 60t + 60

To solve the equation, we'll have to get t on one side of the equals sign and a number on the other. We can get rid of 60 t on the right side by subtracting 60 t from both sides: 80 t - 60 t is 20 t .

Finally, we can get rid of the 20 next to t by dividing both sides by 20 . 60 divided by 20 is 3 .

So t is equal to 3 . The fast train traveled for 3 hours . However, it's not the answer to our problem. Let's look at the original problem again. Pay attention to the last sentence, which is the question we're trying to answer.

Our problem doesn't ask how long either of the trains traveled. It asks what time the second train catches up with the first.

The problem tells us that the slow train left at noon and the fast one left an hour later. This means the fast train left at 1 p.m . From our equations, we know the fast train traveled 3 hours . 1 + 3 is 4 , so the fast train caught up with the slow one at 4 p.m . The answer to the problem is 4 p.m .

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Average Speed Problems

Related Pages Rate, Time, Distance Solving Speed, Time, Distance Problems Using Algebra More Algebra Lessons

In these lessons, we will learn how to solve word problems involving average speed.

There are three main types of average problems commonly encountered in school algebra: Average (Arithmetic Mean) Weighted Average and Average Speed.

How to calculate Average Speed?

The following diagram shows the formula for average speed. Scroll down the page for more examples and solutions on calculating the average speed.

Examples Of Average Speed Problems

Example: John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?

Solution: Step 1: The formula for distance is

Distance = Rate × Time Total distance = 50 × 3 + 60 × 2 = 270

Step 2: Total time = 3 + 2 = 5

Step 3: Using the formula:

Answer: The average speed is 54 miles per hour.

Be careful! You will get the wrong answer if you add the two speeds and divide the answer by two.

How To Solve The Average Speed Problem?

How to calculate the average speed?

Example: The speed paradox: If I drive from Oxford to Cambridge at 40 miles per hour and then from Cambridge to Oxford at 60 miles per hour, what is my average speed for the whole journey?

How To Find The Average Speed For A Round Trip?

Example: On Alberto’s drive to his aunt’s house, the traffic was light, and he drove the 45-mile trip in one hour. However, the return trip took his two hours. What was his average trip for the round trip?

How To Find The Average Speed Of An Airplane With Good And Bad Weather?

Example: Mae took a non-stop flight to visit her grandmother. The 750-mile trip took three hours and 45 minutes. Because of the bad weather, the return trip took four hours and 45 minutes. What was her average speed for the round trip?

How To Relate Speed To Distance And Time?

If you are traveling in a car that travels 80km along a road in one hour, we say that you are traveling at an average of 80kn/h.

Average speed is the total distance divided by the total time for the trip. Therefore, speed is distance divided by time.

Instantaneous speed is the speed at which an object is traveling at any particular instant.

If the instantaneous speed of a car remains the same over a period of time, then we say that the car is traveling with constant speed.

The average speed of an object is the same as its instantaneous speed if that object is traveling at a constant speed.

How To Calculate Average Speed In Word Problems?

Example: Keri rollerblades to school, a total distance of 4.5km. She has to slow down twice to cross busy streets, but overall the journey takes her 0.65h. What is Keri’s average speed during the trip?

How To Use Average Speed To Calculate The Distance Traveled?

Example: Elle drives 169 miles from Sheffield to London. Her average speed is 65 mph. She leaves Sheffield at 6:30 a.m. Does she arrive in London by 9:00 a.m.?

How To Use Average Speed To Calculate The Time Taken?

Example: Marie Ann is trying to predict the time required to ride her bike to the nearby beach. She knows that the distance is 45 km and, from other trips, that she can usually average about 20 km/h. Predict how long the trip will take.

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Speed, Distance & Time Calculator

Use this speed calculator to easily calculate the average speed, distance travelled and the trip duration of a vehicle: car, bus, train, bike, motorcycle, plane etc. Works with miles, feet, kilometers, meters, etc..

Related calculators

• Speed, Distance & Time Calculation
• Average Speed formula
• Distance formula
• Duration (Time) formula
• How to calculate the average speed of a car?

    Speed, Distance & Time Calculation

In order to use the above speed, distance & time calculator, or do such math on your own, you will need to know two out of three metrics: speed, distance, time. You will need to convert the metrics to the same time and distance units, e.g. miles, kilometers, meters, yards, feet, and hours, minutes or seconds. For example, if you have speed in mph (miles per hour), time should also be in hours. If you have distance in kilometers, then speed should also be in km/h (kilometers per hour).

The unit of the result will depend on the units you input, but our speed calculator will conveniently display additional units where appropriate.

    Average Speed formula

The formula for average speed, also called average velocity in physics and engineering, is:

where v is the velocity, d is the distance, and t is the time, so you can read it as Speed = Distance / Time . As noted above, make sure you convert the units appropriately first, or use our speed calculator which does that automatically. The resulting unit will depend on the units for both time and distance, so if your input was in miles and hours, the speed will be in mph. If it was in meters and seconds, it will be in m/s (meters per second).

Example: If you took a plane from New York to Los Angeles and the flight was 5 hours of air time, what was the speed of the plane, given that the flight path was 2450 miles? The answer is 2450 / 5 = 490 mph (miles per hour) average speed. If you want the result in km/h, you can convert from miles to km to get 788.58 km/h.

    Distance formula

The formula for distance, if you know time (duration) and the average speed, is:

Example: If a truck travelled at an average speed of 80 km per hour for 4 hours, how many miles did it cover in that time? To find the miles covered, first, calculate 80 * 4 = 320 km, then convert km to miles by dividing by 1.6093 or by using our km to miles converter to get the answer: 198.84 miles.

    Duration (Time) formula

The time, or more precisely, the duration of the trip, can be calculated knowing the distance and the average speed using the formula:

where d is the distance travelled, v is the speed (velocity) and t is the time, so you can read it as Time = Distance / Speed . Make sure you convert the units so both their distance and time components match, or use our trip duration calculator above which will handle conversions automatically. For example, if you have distance in miles and speed in km/h, you will need to convert speed to mph or distance to kilometers. The time unit of the result will match the time unit of the speed measure, so if it is measured in something per hour, the result will be in hours. If it is measured in some unit per second, the result will be in seconds.

Example: If a train can travel 500 miles with an average speed of 50 miles per hour, how long it would take it to complete a 500-mile route? To find the answer, use the formula and substitute the values, resulting in 500 / 50 = 10 hours.

    How to calculate the average speed of a car?

Say you travelled a certain distance with a car or another vehicle and you want to calculate what its average speed was. The easiest way to do that would be by using the calculator above, but if you prefer, you can also do the math yourself. Either way, you need to know the distance to a satisfactory approximation, for which you can use a map (e.g. Google Maps) to measure the distance from point to point. Make sure you measure closely to the path you took, and not via a straight line, unless you travelled by air in which case that would be a good approximation. Of course, having a GPS reading of the distance would be more precise. Then you need to know the travel time. Make sure you subtract any rests or stops you made from the total trip duration.

If the total distance travelled was 500 miles and the time it took you was 5 hours, then your average speed was 500 / 5 = 100 miles per hour (mph). If the distance was 300 kilometers and it took you 5 hours to cover it, your speed was 300 / 5 = 60 km/h (kilometers per hour).

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Speed Distance Time Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/speed-calculator.php URL [Accessed Date: 13 Jun, 2024].

     Transportation calculators

Speed Distance Time Calculator

Please enter the speed and distance values to calculate the travel time in hours, minutes and seconds.

About Speed Distance Time Calculator

This online calculator tool can be a great help for calculating time basing on such physical concepts as speed and distance. Therefore, in order to calculate the time, both distance and speed parameters must be entered. For the speed , you need to enter its value and select speed unit by using the scroll down menu in the calculator. For distance , you should enter its value and also select the proper length measurement unit from the scroll down menu. You'll receive the result in standard time format (HH:MM:SS).

Time Speed Distance Formula

Distance is equal to speed × time. Time is equal Distance/Speed.

Calculate Time from Distance and Speed Examples

Recent comments.

One of the best tools I've found for the calculations.

Going 65mph for 30 seconds how far would you get? None of these formulas work without distance. How would I find the distance from time and speed?

if i travel 0.01 inches per second and I need to travel 999999999 kilometers, it takes 556722071 Days and 20:24:34 WHAT

4. How long does it take to do 100m at 3kph ? No I thought you would just divide 100 ÷ 3 = which 33.33333 so 33 seconds or so I thought. But apparently it 2 mins.

This was the best tool ive ever used that was on point from speed to distance and time Calculator

This was somewhat unhelpful as I know the time and distance, but not the speed. Would be helpful if this calculator also could solve the other two as well.

If a total distance of 2 miles is driven, with the first mile being driven at a speed of 15mph, and the second mile driven at a speed of 45 mph: What is the average speed of the full 2 mile trip?

hi sorry im newly introduced to this and i dont understand how to use it but in need to find the distance if i was travelling in the average speed of 15km/hr in 4 hours how far would i travel

D= 697 km T= 8 hours and 12 minutes S= ?

if a train is going 130 miles in 50 minutes, how fast is it going in miles per hour ??

whats the speed if you travel 2000 miles in 20hours?

How long would it take me to drive to Mars at 100 miles per hour and how much gas would I use in a 2000 Ford Mustang000000/ Also, how much CO2 would I release into the air?

great tool helped me alot

A car can go from rest to 45 km/hr in 5 seconds. What is its acceleration?

Guys how much time will a cyclist take to cover 132 METRES With a speed of 8 km/ph

@Mike Depends on how fast that actually is. For every 10 mph above 60, but below 120, you save 5 seconds a mile. But between the 30-60 area, every ten saves 10 seconds a mile (if I am remembering correctly), and every 10 between 15-30 is 20 seconds. Realistically, it isn't likely isn't worth it, unless it is a relatively straight drive with no stops, in which case you will likely go up a gear for the drive and thus improve gas efficiency for the trip. Only really saves time if it is over long trips 300+ miles (in which case, assuming you were on the interstate) that 5 seconds a mile would save you 25 minutes from the drive, making it go from 4h35m to 4h10m. For me, I have family across the U.S., so family visits are usually 900-1400 miles. Even only driving 5 above usually saves me 90-150 minutes or so (since I often have stretches where I drive on US highways which have 55 mph speed limits)

I would like to know if driving fast is worth it for short trips. If I drive 10 MPH over the speed limit for 10 miles, how much time do i save ? Is there an equation for that ?

it helps me in lot of stuff

awesome, helped me notice how long my taiga (electric seedoo) is going to last.

SOLUTION: a man decides to travel 80 kilometer in 8 hours partly by foot and partly on a bicycle. if his speed on a foot is 8 km/hr and on bicycle is 16 km/hr what distance would he travel o

Speed and Time Calculator

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Speed of Light Calculator

Table of contents

With this speed of light calculator, we aim to help you calculate the distance light can travel in a fixed time . As the speed of light is the fastest speed in the universe, it would be fascinating to know just how far it can travel in a short amount of time.

We have written this article to help you understand what the speed of light is , how fast the speed of light is , and how to calculate the speed of light . We will also demonstrate some examples to help you understand the computation of the speed of light.

What is the speed of light? How fast is the speed of light?

The speed of light is scientifically proven to be the universe's maximum speed. This means no matter how hard you try, you can never exceed this speed in this universe. Hence, there are also some theories on getting into another universe by breaking this limit. You can understand this more using our speed calculator and distance calculator .

So, how fast is the speed of light? The speed of light is 299,792,458 m/s in a vacuum. The speed of light in mph is 670,616,629 mph . With this speed, one can go around the globe more than 400,000 times in a minute!

One thing to note is that the speed of light slows down when it goes through different mediums. Light travels faster in air than in water, for instance. This phenomenon causes the refraction of light.

Now, let's look at how to calculate the speed of light.

How to calculate the speed of light?

As the speed of light is constant, calculating the speed of light usually falls on calculating the distance that light can travel in a certain time period. Hence, let's have a look at the following example:

• Source: Light
• Speed of light: 299,792,458 m/s
• Time traveled: 100 seconds

You can perform the calculation in three steps:

Determine the speed of light.

As mentioned, the speed of light is the fastest speed in the universe, and it is always a constant in a vacuum. Hence, the speed of light is 299,792,458 m/s .

Determine the time that the light has traveled.

The next step is to know how much time the light has traveled. Unlike looking at the speed of a sports car or a train, the speed of light is extremely fast, so the time interval that we look at is usually measured in seconds instead of minutes and hours. You can use our time lapse calculator to help you with this calculation.

For this example, the time that the light has traveled is 100 seconds .

Calculate the distance that the light has traveled.

The final step is to calculate the total distance that the light has traveled within the time . You can calculate this answer using the speed of light formula:

distance = speed of light × time

Thus, the distance that the light can travel in 100 seconds is 299,792,458 m/s × 100 seconds = 29,979,245,800 m

What is the speed of light in mph when it is in a vacuum?

The speed of light in a vacuum is 670,616,629 mph . This is equivalent to 299,792,458 m/s or 1,079,252,849 km/h. This is the fastest speed in the universe.

Is the speed of light always constant?

Yes , the speed of light is always constant for a given medium. The speed of light changes when going through different mediums. For example, light travels slower in water than in air.

How can I calculate the speed of light?

You can calculate the speed of light in three steps:

Determine the distance the light has traveled.

Apply the speed of light formula :

speed of light = distance / time

How far can the speed of light travel in 1 minute?

Light can travel 17,987,547,480 m in 1 minute . This means that light can travel around the earth more than 448 times in a minute.

Speed of light

The speed of light in the medium. In a vacuum, the speed of light is 299,792,458 m/s.

clock This article was published more than  43 years ago

On the Road, Again?

Wynema Collins Sharman has a bottle filled with water from the Atlantic Ocean that she wanted to pour into the Pacific, as sort of symbolic union of East and West.

Ordinarily that would be no great feat. But 54-year-old Sharman, known as Winnie to friends, had hoped to hold her small ceremony by personally carrying the bottle on a coast-to-coast walk from Virginia Beach to Seal Beach, Calif.

That's past tense for Sharman. On Sept. 10, she was forced to abandon her walk -- temporarily at least -- in Madison, Ark., after completing nearly 1,100 miles of the 3,000-mile hike.

Sharman, who lives in Arlington, said she took off her sneakers when $1,100 from commercial sponsors dried up and her companion-driver, LaVonne Brandts, a retired Arlington nurse, decided to go home because she missed her husband.

So after 70 days of walking in the grueling sun, losing 22 pounds and dipping into family coffers to meet $3,000 worth of expenses the sponsors didn't cover, Sharman decided to head home in search of more financial support and another driver.

"I hoped to be the first woman to walk from the Atlantic to the Pacific, and I still have that hope," said Sharman, who wants to raise another $5,000 to complete the trip.

The Guinness Book of World Records measures cross-country walks in terms of speed, not the sex of the walker, and mentions no woman completing such a trip.

Because Sharman wants to finish the trip and be home before Christmas, she said she needs to line up sponsors this week or put off the rest of the expected 100-day hike until next year.

While only a few companies have contributed money, others have provided supplies such as vitamins, T-shirts, sneakers, sun-shielding cosmetics and a much-used foot massager.

But food, gas and car repairs claimed their toll. Sharman said she also was paying expenses for Brandts, who drove ahead a few miles each day, waiting for Sharman to catch up on foot. At night, Brandts would drive herself and Sharman to a motel, then drive Sharman back to her last stopping point the next morning.

Sharman's original sponsor, whom she won't name, had promised $5,000, a van and clothing, but withdrew the offer three days before the trip started June 30.

"It was right after the Rosie Ruiz incident, and one of (the sponsor's) lawyers was afraid I'd leave them with egg on their face," said Sharman, referring to the runner who took a "shortcut" to the finish line of the Boston Marathon and was disqualified as the first-place female finisher.

But Sharman, who works part-time at a firm that helps people obtain visas, hopes her progress so far will assure potential sponsors that she is serious.

The most difficult parts of her walk, she said, were scaling Stuart Mountain in the Blue Ridge and crossing high bridges over the Tennessee and Mississippi rivers.

"I'm a little afraid of heights, so I said the Lord's Prayer and the 23rd Psalm all the way across," she laughed.

Besides undertaking the project for fun and a chance to be the first woman to walk coast-to-coast, Sharman said she had other reasons: "I thought it would be a legacy for my children and grandchildren, to show them that if they want to do something badly enough, they could -- and to finish what they start.

"I also wanted to show people that people in my age bracket aren't old."

Flight Time Calculator

Flying time between cities.

Travelmath provides an online flight time calculator for all types of travel routes. You can enter airports, cities, states, countries, or zip codes to find the flying time between any two points. The database uses the great circle distance and the average airspeed of a commercial airliner to figure out how long a typical flight would take. Find your travel time to estimate the length of a flight between airports, or ask how long it takes to fly from one city to another.

You can also search for the closest airport to any city in the world or check the flying distance between airports. If you're thinking about a road trip, compare the driving time for the same route.

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