### 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

**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 h. How much time will he take to drive both ways? (UPSC 2013)**

a. Two house

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. 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

**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 kms

b. 2 kms

c. 3 kms

d. 3.5 kms

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