A car travels 240 km in 4 hours. What is its speed?

60 km/h. Speed = 2404 = 60 km/h.

Convert 72 km/h into metres per second.

20 m/s. Multiply by 518: 72 518 = 20 m/s.

A student walking to school at 5 km/h is 6 minutes late; at 6 km/h he is 2 minutes early. How far is the school?

4 km. The two speeds differ in time by 6 + 2 = 8 minutes = 215 h. So d5 - d6 = 215, i.e. d30 = 215, giving d = 4 km.

A train covers a distance in 2 hours at 60 km/h. At what speed must it travel to cover the same distance in 1 hour 30 minutes?

80 km/h. The distance is 60 2 = 120 km. To cover it in 1.5 hours the speed must be 1201.5 = 80 km/h.

Town P and town Q are 250 km apart. A car leaves P towards Q at 40 km/h and, at the same moment, another leaves Q towards P at 60 km/h. After how long do they meet?

2.5 hours. They approach each other at 40 + 60 = 100 km/h, so they meet after 250100 = 2.5 hours.

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Quantitative Aptitude · Time, Work & Distance

Time and Distance — Questions & Answers

Every time-and-distance question is a use of distance = speed × time. Keep units consistent, use average speed for multi-leg trips, and use relative speed when two bodies move together or apart.

5 solved questions
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Step-by-step AI walkthroughs
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Key formulas included

Key formulas

$\text{Distance} = \text{Speed} \times \text{Time}$
$x$ km/h $= x \times \dfrac{5}{18}$ m/s; and $x$ m/s $= x \times \dfrac{18}{5}$ km/h
Average speed over equal distances at $u$ and $v$ : $\dfrac{2uv}{u+v}$

5 solved Time and Distance questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
A car travels 240 km in 4 hours. What is its speed?
4 steps · reveal one at a time
1. Step 1: Identify Given Information
  The question tells us the car travels a distance of $240$ km. It completes this journey in a time of $4$ hours. We need to find the car's speed.
2. Step 2: Recall Speed Formula
  To find the speed, we use the basic formula: Speed $= \text{Distance} \div \text{Time}$ . This formula helps us determine how fast an object is moving over a certain period.
3. Step 3: Calculate Speed
  Now, substitute the given values into the formula. Speed $= 240 \text{ km} \div 4 \text{ hours}$ . Perform the division to find the car's speed in kilometers per hour.
4. Step 4: The answer
  So the answer is (C) 60 km/h. Dividing the total distance of $240$ km by the total time of $4$ hours gives us $60$ km/h.
02
Convert 72 km/h into metres per second.
4 steps · reveal one at a time
1. Step 1: Identify the conversion
  The question asks us to convert a speed given in kilometres per hour (km/h) into metres per second (m/s). This is a common unit conversion.
2. Step 2: Recall conversion factor
  To convert a speed from km/h to m/s, you can multiply the value by the fraction $\frac{5}{18}$ . This factor simplifies the conversion process.
3. Step 3: Perform the calculation
  Now, let's apply this conversion factor to the given speed of 72 km/h. We calculate $72 \times \frac{5}{18}$ . This simplifies to $4 \times 5 = 20$ .
4. Step 4: The answer
  So the answer is (B) 20 m/s. After multiplying 72 by $\frac{5}{18}$ , we get 20, which is the speed in metres per second.
03
A student walking to school at 5 km/h is 6 minutes late; at 6 km/h he is 2 minutes early. How far is the school?
5 steps · reveal one at a time
1. Step 1: Understand the problem
  We have two scenarios for the student's walk to school, each with a different speed and a different arrival time relative to the correct time. We need to find the distance to the school.
2. Step 2: Calculate time difference
  When walking at 5 km/h, the student is 6 minutes late. At 6 km/h, they are 2 minutes early. The total difference in travel time between these two speeds is $6 + 2 = 8$ minutes. Convert this to hours: $8 \text{ minutes} = \frac{8}{60} = \frac{2}{15}$ hours.
3. Step 3: Formulate the equation
  Let $d$ be the distance to school. The time taken is distance/speed. So, at 5 km/h, time is $\frac{d}{5}$ . At 6 km/h, time is $\frac{d}{6}$ . The difference in these times is $\frac{2}{15}$ hours: $\frac{d}{5} - \frac{d}{6} = \frac{2}{15}$ .
4. Step 4: Solve for distance
  To solve $\frac{d}{5} - \frac{d}{6} = \frac{2}{15}$ , find a common denominator for the left side: $\frac{6d - 5d}{30} = \frac{2}{15}$ . This simplifies to $\frac{d}{30} = \frac{2}{15}$ . Multiply both sides by 30 to find $d = 30 \times \frac{2}{15} = 4$ km.
5. Step 5: The answer
  So the answer is (A) 4 km, because the calculated distance to the school based on the time differences at varying speeds is 4 km.
04
A train covers a distance in 2 hours at 60 km/h. At what speed must it travel to cover the same distance in 1 hour 30 minutes?
4 steps · reveal one at a time
1. Step 1: Calculate Total Distance
  First, let's find the total distance the train covers. We know it travels at $60$ km/h for $2$ hours. Use the formula: Distance = Speed $\times$ Time. So, the distance is $60 \times 2 = 120$ km.
2. Step 2: Convert New Time
  The train needs to cover the same distance in $1$ hour $30$ minutes. It's easier to work with hours only, so convert $30$ minutes to hours. $30$ minutes is $0.5$ hours. Therefore, the new time is $1 + 0.5 = 1.5$ hours.
3. Step 3: Calculate Required Speed
  Now we know the distance ( $120$ km) and the new time ( $1.5$ hours). To find the required speed, use Speed = Distance $\div$ Time. So, the new speed must be $120 \div 1.5 = 80$ km/h.
4. Step 4: The answer
  So the answer is (C) 80 km/h, because this speed allows the train to cover the $120$ km distance in $1.5$ hours.
05
Town P and town Q are 250 km apart. A car leaves P towards Q at 40 km/h and, at the same moment, another leaves Q towards P at 60 km/h. After how long do they meet?
4 steps · reveal one at a time
1. Step 1: Identify key facts
  We have two towns, P and Q, 250 km apart. Two cars start simultaneously, moving towards each other. Car from P travels at $40 \text{ km/h}$ , and car from Q at $60 \text{ km/h}$ .
2. Step 2: Calculate relative speed
  Since the cars are moving towards each other, their speeds combine to determine how quickly the distance between them closes. This is called their relative speed. Add their individual speeds: $40 \text{ km/h} + 60 \text{ km/h} = 100 \text{ km/h}$ .
3. Step 3: Determine meeting time
  To find out when they meet, divide the total distance by their combined relative speed. The time taken is $\text{Distance} \div \text{Relative Speed}$ . So, $250 \text{ km} \div 100 \text{ km/h} = 2.5 \text{ hours}$ .
4. Step 4: The answer
  So the answer is (B) 2.5 hours, because the cars close the 250 km distance at a combined rate of 100 km/h.

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