Time and Distance Aptitude

Time and Distance problems are a crucial part of aptitude tests and often involve calculations based on the relationship between speed, distance, and time. Understanding these concepts is essential for solving various real-life problems, such as travel planning, speed optimization, and estimating arrival times.

1. A car travels at a speed of 60 km/hr. How many kilometers will it travel in 1.5 hours?

Distance = Speed × Time = 60 km/hr × 1.5 hrs = 90 km.

2. If a train travels at 80 km/hr, how long will it take to cover a distance of 160 kilometers?

Time = Distance / Speed = 160 km / 80 km/hr = 2 hours.

3. A cyclist covers a distance of 45 km in 3 hours. What is his speed?

Speed = Distance / Time = 45 km / 3 hrs = 15 km/hr.

4. Two cities are 350 km apart. A train travels from the first city to the second at a speed of 70 km/hr and returns at a speed of 50 km/hr. What is the average speed for the entire trip?

Average speed = Total distance / Total time
Total distance = 350 km + 350 km = 700 km
Total time = 350 km / 70 km/hr + 350 km / 50 km/hr = 5 hrs + 7 hrs = 12 hrs
Average speed = 700 km / 12 hrs = 58.33 km/hr ≈ 58 km/hr.

5. A car takes 4 hours to cover a distance of 240 km. What is its average speed?

Average speed = Total distance / Total time = 240 km / 4 hrs = 60 km/hr.

6. A person walks at a speed of 5 km/hr and runs at a speed of 10 km/hr. If he covers 15 km by walking and running for a total of 2.5 hours, how much distance did he cover by running?

Let the distance covered by running be x km. Then, distance covered by walking = 15 - x km.
Time for running = x / 10 hrs, Time for walking = (15 - x) / 5 hrs.
Total time = 2.5 hrs.
x/10 + (15 - x)/5 = 2.5
Solve for x to get x = 10 km.

7. Two trains start at the same time from two stations 300 km apart and travel towards each other at speeds of 60 km/hr and 90 km/hr respectively. After how many hours will they meet?

Relative speed = 60 km/hr + 90 km/hr = 150 km/hr.
Time to meet = Distance / Relative speed = 300 km / 150 km/hr = 2 hours.

8. A bus covers a certain distance at a speed of 50 km/hr in 5 hours. To cover the same distance in 3 hours, what should be the speed?

Distance = Speed × Time = 50 km/hr × 5 hrs = 250 km.
Required speed = Distance / New time = 250 km / 3 hrs ≈ 83.33 km/hr.

9. A man completes a journey in 10 hours. He travels the first half at 20 km/hr and the second half at 30 km/hr. Find the total distance.

Let the total distance be x km.
Time for first half = x/2 / 20 hrs, time for second half = x/2 / 30 hrs.
Total time = 10 hrs.
x/2 / 20 + x/2 / 30 = 10
Solve for x to get x = 240 km.

10. A boy cycles at 12 km/hr and reaches his school 10 minutes late. If he cycles at 15 km/hr, he reaches 5 minutes early. Find the distance to his school.

Let the distance be x km.
Difference in time = 15 minutes = 1/4 hour.
x/12 - x/15 = 1/4
Solve for x to get x = 7 km.

11. A train 100 meters long crosses a platform 200 meters long in 20 seconds. What is the speed of the train?

Distance = 100 meters + 200 meters = 300 meters.
Speed = Distance / Time = 300 meters / 20 seconds = 15 m/s.
Speed in km/hr = 15 × 18/5 = 54 km/hr.

12. A person travels from A to B at 40 km/hr and returns by increasing his speed 25%. What is his average speed for both trips?

Speed on return trip = 125% of 40 km/hr = 50 km/hr.
Average speed = 2 × (40 × 50) / (40 + 50) = 44 km/hr.

13. Two friends start from the same point and walk at 4 km/hr and 5 km/hr respectively in the same direction. What will be the distance between them after 3 hours?

Relative speed = 5 km/hr - 4 km/hr = 1 km/hr.
Distance after 3 hours = 1 km/hr × 3 hrs = 3 km.

14. A car covers a distance in 50 minutes. If it travels at a speed of 48 km/hr on an average, find the distance.

Time = 50 minutes = 50/60 hours = 5/6 hours.
Distance = Speed × Time = 48 km/hr × 5/6 hrs = 40 km.

15. Two trains travel in the same direction at 50 km/hr and 32 km/hr respectively. A man in the slower train observes that the faster train passes him in 18 seconds. The length of the faster train is:

Relative speed = (50 - 32) km/hr = 18 km/hr = 18 × 5/18 m/s = 5 m/s.
Length of the faster train = Relative speed × Time = 5 m/s × 18 s = 90 m.

16. A person walks at 5 km/hr for 6 km and 4 km/hr for 12 km. What is the average speed for the entire distance?

Total distance = 6 km + 12 km = 18 km.
Total time = 6 km / 5 km/hr + 12 km / 4 km/hr = 1.2 hrs + 3 hrs = 4.2 hrs.
Average speed = Total distance / Total time = 18 km / 4.2 hrs = 4.29 km/hr ≈ 4.2 km/hr.

17. A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third with a speed of 20 km/hr, and the last one-third with a speed of 60 km/hr. Find the average speed for the whole journey.

Let the total distance be x km.
Time for the first one-third = (x/3) / 10 hrs, for the second one-third = (x/3) / 20 hrs, and for the last one-third = (x/3) / 60 hrs.
Total time = x/30 + x/60 + x/180 = x/15 hrs.
Average speed = Total distance / Total time = x / (x/15) = 15 km/hr.

18. A man covers a certain distance on a toy train. If the train moved 4 km/hr faster, it would take 30 minutes less. If it moved 2 km/hr slower, it would take 20 minutes more. Find the distance.

Let the distance be x km and the original speed be y km/hr.
x/y - x/(y + 4) = 1/2, x/y - x/(y - 2) = 1/3.
Solve the two equations to find x.

19. Two cars start from the same place in opposite directions. One goes towards North at 60 km/hr and the other goes towards South at 40 km/hr. After how many hours will they be 150 km apart?

Relative speed = 60 km/hr + 40 km/hr = 100 km/hr.
Time = Distance / Speed = 150 km / 100 km/hr = 1.5 hours.

20. A cyclist and a jogger start from two points A and B towards each other and meet after 6 hours. The cyclist started from A at a speed of 4 km/hr and the jogger started from B at a speed of 3 km/hr. Find the distance between A and B.

Relative speed = 4 km/hr + 3 km/hr = 7 km/hr.
Total distance = Time × Relative speed = 6 hrs × 7 km/hr = 42 km.