### Introduction

• The mathematical model that describes motion has three variables, namely: Speed, Time and Distance. T
• he interrelationship between these three is also the most important formula for this chapter, namely:

Speed X Time = Distance (Equation for the description of one motion of one body)

• The above equation is the mathematical description of the movement of a body. In complex problems, students tend to get confused regarding the usage of this equation and often end up mixing up the speed, time and distance of different motions of different bodies.
• It must be mentioned here that this formula is the cornerstone of the chapter Time, Speed and Distance.

### Note

• Basic Time and Distance Problems.
• Average Speed = Total Distance covered/Total time taken
• Relative Speed.
• Problems Based on Trains.
• Boats And Streams
• Distance = Speed * Time
• km/hr to m/sec and Vice Versa (Factor Of 5/18).
• Average Speed is Not Averages of Speed.
• Average Speed = Total Distance Travelled/Total Time Taken
• Note: All Units Must Be Same**.

### Practice Questions :

1. A man in a car can count 25 telephone posts in 1min. If they are known to be 40m apart, then at what speed is the car travelling?
a. 52.4 km/h
b. 57.6 km/h
c. 48.2 km/h
d. 44.9 km/h

2. A person travelled a distance of 50 km in 8h. He covered a part of the distance on foot @ of 4km/h and a part on bicycle @ 10km/h. How much distance did he travel on foot?
a. 10
b. 30
c. 20
d. 15

3. Two cities A and B 360km apart. A car goes from A to B @40km/h and B to A @ 60k/h. Find average speed.
a. 45 km/hr
b. 48 km/hr
c. 50 km/hr
d. 55 km/hr

4. Mr. Kumar drives to work at an average speed of 48 k/h. The time taken to cover the 60% of the distance is 10 min more than the time taken to cover the remaining distance. How far is the office?
a. 30 km
b. 40 km
c. 48 km
d. 56 km

5. A bus is moving 30km/h ahead of a car moving at 50 km/h. How many km apart are they if it takes 15 min for the car to catch the bus?
a. 5 km
b. 7.5 km
c. 12.5 km
d. 45 km

6. Two trains leave Delhi for Dehradun at 10 and 10:30 am respectively and travel @ 120 k/h and 150 k/h resp. How many km from Delhi will the two trains meet?
a. 300 km
b. 200 km
c. 150 km
d. 400 km

7. Shree decided to cover a distance of 6 km in 84 minutes. He decided to cover two thirds of the distance at 4 km / hr and the remaining at some different speed. Find the speed after the two third distance has been covered?
a. 5 kmph
b. 6 kmph
c. 7 kmph
d. 3 kmph

8. A worker reaches his factory 3 min late walking @ 5 km/h and 7 min early walking @ 6k/h. The distance between the house and the factory is? (UPSC 2014)
a. 3 km
b. 4 km
c. 5 km
d. 6 km

9. A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 metres ahead of the policeman, then the time required for the policeman to catch the thief will be. (UPSC 2013)
a. 2 min
b. 3 min
c. 4 min
d. 6 min

10. A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed? (UPSC 2013)
a. 24
b. 33
c. 42
d. 66

11. A person can walk a certain distance and drive back in 6 h. He can also walk both ways in 10 hours. How much time will he take to drive both ways? (UPSC 2013)
a. Two hours
b. Two and a half hours
c. Five and a half hours
d. Four hours

12. Two cars start towards each other, from two places A and B which are at a distance of 160 km. They start at the same time 08 :10 AM. If the speeds of the cars are 50 km and 30 km per hour respectively, they will meet each other at (UPSC 2014)
a. 10:10 AM
b. 10:30 AM
c. 11:10 AM
d. 11:20 AM

13. In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time? (UPSC 2015)
a. 25:21
b. 25:20
c. 5:3
d. 5:7

14. A freight train left Delhi for Mumbai at an average speed of 40 km/hr. Two hours later an express train left Delhi for Mumbai following the freight train on a parallel track at an average speed of 60 km/hr. How far from Delhi would the express train meet the freight train?
(UPSC 2017)

a. 480 km
b. 260 km
c. 240 km
d. 120 km

15. Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds? (UPSC 2018)
a. 6:5
b. 4:3
c. 6:1
d. 4:2

**16. While going to office, Sunil travels at a speed of 30 kmph and on his way back, he travels at a speed of 45 kmph. What is his average speed of the whole journey? **
a. 45 kmph
b. 36 kmph
c. 32 kmph
d. 44 kmph

17. X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?
(UPSC 2019)

a. 20
b. 25
c. 30
d. 35

18. A man takes half time in moving a certain distance downstream than upstream. What is the ratio between rate in still water and rate of current? (UPSC 2020)
a. 1:2
b. 2:1
c. 1:3
d. 3:1

19. A car travels from a place X to place Y at an average speed of V km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey
(UPSC 2020)

a. is less than v km/hr
b. lies between v and 2v km/hr
c. lies between 2v and 3v km/hr
d. lies between 3v and 4v km/hr

20. X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3:2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)? (UPSC 2022)
a. 2
b. 3
c. 4
d. 5

21. Shaym and Ram travel the same distance at the rate of 6 km per hour and 10 km per hour respectively. If Shaym takes 30 minutes longer than Ram, the distance travelled by each is
a. 6 km
b. 10 km
c. 7.5 km
d. 20 km

22. If Varun had walked 1 km/h faster, he would have taken 10 minutes less to walk 2 kilometre. What is Varun’s speed of walking?
a. 1 kmph
b. 2 kmph
c. 3 kmph
d. 6 kmph

23. Walking at ¾ of his normal speed, a man takes 2(1/2) hours more than the normal time. Find the normal time.
a. 7.5 h
b. 6 h
c. 8 h
d. 12 h

24. Rajdhani Express travels 650 km in 5 h and another 940 km in 10 h. what is the average speed of train?
a. 1590 km/h
b. 168 km/h
c. 106 km/h
d. 126 km/h

25. A motor car dose a journey in 17.5 hours, covering the first half at 30 km/h and the second half at 40 km/h. Find the distance of the journey.
a. 684 km
b. 600 km
c. 120 km
d. 540 km

26. Walking at ¾ of his usual speed, a man is 16 minutes late for his office. The usual time taken by him to cover that distance is
a. 48 minutes
b. 60 minutes
c. 42 minutes
d. 62 minutes

27. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
a. 70 km/hr
b. 75 km/hr
c. 84 km/hr
d. 87.5 km/hr

28. If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
a. 150 km
b. 156 km
c. 162 km
d. 168 km

29. Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
a. 15 mins
b. 20 mins
c. 25 mins
d. 30 mins

30. Sagar was riding bike towards north, turned left road 1 km turns towards left & road 2 kms found himself 1 km west of starting. How far did he ride north?
a. 1.5 km
b. 2 km
c. 3 km
d. 3.5 km

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