Time Speed and Distance – 3/5Relative Speed and Races

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Puzzle :

If A goes from his home 60 km due South, 60 km due East, 60 km due

North he lands up at his home again. Where was he on the Earth ?

Relative Speed

Case 1: When one object is moving and the other is stationary the relative speed

between them is the speed of the moving object.

For eg. when a train crosses a stationary person on a platform the relative speed

of the train and the person will be the speed of the train

Relative Speed

Case 2: When two objects are moving in opposite directions the relative speed

between them is the sum of their speeds.

For eg. the realtive speed between two trains moving towards each other is the

sum of their individual speeds.

Relative Speed

Case 3: When two bodies are moving in the same direction the realtive speed

between them is the difference of their speeds.

For eg. the relative speed between two trains moving in the same direction on

parallel tracks is the difference between their individual speeds.

1. A train crosses a 250 m long platform. The speed of the train is 36 km/hr. The totaltime taken by the train to cross the platform is 35 s. The length of the train is

(1) 120 m

(2) 110 m

(3) 125 m

(4) 100 m

(5) None of these

2. A train 150 m long takes 9 sec to cross a man walking at 8 kmph in a direction

opposite to that of the train. Find the speed (in km/hr) of the train.

(1) 72

(2) 60

(3) 54

(4) 52

3. Two trains are running on parallel tracks and they travel at the rates of 25 kmph and

30 kmph. If the first train leaves an hour earlier than the second train, how long will it

take for the second train to catch up with the first train?

(1) 3 hr (2) 4 hr (3) 6 hr (4) 5 hr (5) 7 hrc

4. Two trains start from A and B and head towards B and A respectively. Train from A

starts at 11 p.m. and reaches B at 5 p.m. next day. Train from B starts at 10 p.m. the

same day on which the train starts from station A and reaches A at 6 a.m. the next day.

At what time (approximately) will they cross each other?

(1) 4 a.m.

(2) 3.55 a.m.

(3) 2.51 a.m.

(4) 4.05 a.m.

(5) 3.51 a.m.

5. Train X departs from station A at 11 a.m. for station B, which is 180 km far from A. Train

Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70

km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average

speed of 50 km/hr, but has to stop for 15 min at station C, which is 60 km away from

station B, enroute to station A. Ignoring the lengths of the trains, what is the distance, to

the nearest kilometre, from station A to the point where the trains cross each other? (CAT

2001)

(1) 112 km (2) 118 km (3) 120 km (4) None of these

6. Two trains of lengths 200 m and 250 m are travelling in opposite directions. They cross

each other completely in 20 seconds. If they were travelling in same direction, the time

taken by the faster train to cross the slower train would be 50 seconds. Find the ratio of

the speed of the faster train to that of the slower train?

(1) 43 : 11 (2) 21 : 9

(3) 23 : 7 (4) 35 : 11

7. Two trains travel towards each other on the same track at speeds of 60 kms/hr and 80

kms/hr, separated initially by a distance of 280 km. A bird flying from the faster train to the

slower train and back at a speed of 150 kms/hr continues doing so till the trains collide.

What is the total distance flown by the bird till the trains collide?

(1) 300 km (2) 230 km

(3) 160 km (4) None of these

8. In previous question, calculate the total distance traversed by the bird in the direction of

the faster train. Also find how many laps are made by the bird?

(1) 180 km, infinity (2) 200 km, 200

(3) 230 km, infinity (4) None of these

9. Two cities A and B are located in different time zones separated by a distance of 2000 km

from each other, A being located to the east of B. An aircraft departs from city A at 8 a.m.

(local time of city A) and arrives at B at 11 am (local time of B) the same day. While flying

from A to B the aircraft engine has to perform against a steady wind blowing at a speed of

100 km/hr. The next day the same aircraft departs from B to A at 8 am (local time of B) and

arrives in at A at 2 pm (local time of A) the same day. However during the return flight it does

not have to fly with or against any wind. Find the speed of the plane (assume that the plane

maintains the same speed on both trips) and also the time difference between A and B.

(CAT 2007)

(1) 500 km/hr, 2hrs (2) 400 km/hr, 1hr

(3) 450 km/hr, 1.5hrs (4) None of these

Linear races

Concept of Head start:

In a race of X metres, if A gives B a head start of Y meters then B will start the

race Y metres ahead of A i.e. if A runs for entire X metres then B will only run

for X-Y metres.

In a race of X metres, if A gives B a head start of t seconds then A will start the

race t seconds after B.

1. In a race of 1000 m, A beats B by 200 m and B beats C by 200 m. By what

distance does A beat C?

(1) 400 m (2) 350 m

(3) 360 m (4) 380 m

2. In a race of 1000 m, A beats B by 200 m. In a race of 1500 m B beats C by 300 m.

By what distance will A beat C in a 2000 m race?

(1) 600 m (2) 700 m

(3) 720 m (4) 800 m

3. In a race of 1000 m, A beats B by 200 m or 20 seconds. What is the speed of A?

(1) 12.5 m/sec (2) 13 m/sec

(3) 15 m/sec (4) 11.5 m/sec

4. P beats Q by 20 m in a 120 m race, and Q beats R by 24 m in the same race. By

what distance will P beat R in a race of 150 m?

(1) 54 m (2) 50 m (3) 48 m (4) 45 m

5. In a 300 m race, the ratio of the speeds of two contestants A and B is 2 : 3. At a point

in the race, B was 60 m ahead of A. Find the distance covered by B then ?

(1) 180 m

(2) 120 m

(3) 240 m

(4) 220 m

6. In a 500 m race, the ratio of the speeds of two contestants A and B is 2 : 3. If A has a

head start of 170 m, then A wins by

(1) 5 m

(2) 10 m

(3) 15 m

(4) 20 m

7. Karan and Arjun run a 100-meter race, in which Karan beats Arjun by 10 metres. To

do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100

metre race. They both run at their earlier speeds. Which of the following is true in

connection with the second race?

(1) Karan and Arjun reach the finishing line simultaneously.

(2) Arjun beats Karan by 10 metres

(3) Arjun beats Karan by 11 metres.

(4) Karan beats Arjun by 1 metre.

8. Three runners A, B and C run a race, with runner A finishing 12 m ahead of runner B

and 18 m ahead of runner C, while runner B finishes 8 m ahead of runner C. Each

runner travels the entire distance at a constant speed. What was the length of the race?

[CAT 2001]

(1) 36 m (2) 48 m (3) 60 m (4) 72 m

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