Speed, Time and Distance
 A man standing on a platform finds that a train takes 3 seconds to pass him and another train of the same length moving in the opposite direction, takes 4 seconds. The time taken by the trains to pass each other will be


2 3 seconds 7 
3 3 seconds 7 
4 3 seconds 7 
5 3 seconds 7


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Let the length of each train be x metres
Then, Speed of first train = x m/sec 3 Speed of second train = x m/sec 4
They are moving in opposite directions∴ Required time = x + x 3 4 = 4x + 3x = 7x m./sec. 12 12
Total length = x + x = 2 x m.∴ Time taken = 2x 7x 12 = 24 7 = 3 3 sec. 7 Correct Option: B
Let the length of each train be x metres
Then, Speed of first train = x m/sec 3 Speed of second train = x m/sec 4
They are moving in opposite directions∴ Required time = x + x 3 4 = 4x + 3x = 7x m./sec. 12 12
Total length = x + x = 2 x m.∴ Time taken = 2x 7x 12 = 24 7 = 3 3 sec. 7
 Two trains 108 m and 112 m in length are running towards each other on the parallel lines at a speed of 45 km/hr and 54 km/ hr respectively. To cross each other after they meet, it will take

 12 sec
 9 sec
 8 sec
 10 sec

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Relative speed = 45 + 54 = 99 kmph
= 99 × 5 m/sec. 18 or 55 m/sec. 2 ∴ Required time = 108 + 112 55 2 = 220 × 2 = 8 seconds 55 Correct Option: C
Relative speed = 45 + 54 = 99 kmph
= 99 × 5 m/sec. 18 or 55 m/sec. 2 ∴ Required time = 108 + 112 55 2 = 220 × 2 = 8 seconds 55
 Two trains start from station A and B and travel towards each other at speed of 16 miles/ hour and 21 miles/ hour respectively. At the time of their meeting, the second train has travelled 60 miles more than the first. The distance between A and B (in miles) is :

 444
 496
 333
 540

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Let the trains meet after t hours
Then, 21t – 16t = 60
⇒ 5t = 60 ⇒ t = 12 hours
∴ Distance between A and B
= (16 + 21) × 12
= 37 × 12 = 444 miles
Second Method :
Here, a = 21, b = 16, d = 60Distance between A and B = a + b × d a − b = 21 + 16 × 60 21 − 16 = 37 × 60 5
= 37 × 12 = 444 milesCorrect Option: A
Let the trains meet after t hours
Then, 21t – 16t = 60
⇒ 5t = 60 ⇒ t = 12 hours
∴ Distance between A and B
= (16 + 21) × 12
= 37 × 12 = 444 miles
Second Method :
Here, a = 21, b = 16, d = 60Distance between A and B = a + b × d a − b = 21 + 16 × 60 21 − 16 = 37 × 60 5
= 37 × 12 = 444 miles
 Two trains 150 m and 120 m long respectively moving from opposite directions cross each other in 10 secs. If the speed of the second train is 43.2 km/hr, then the speed of the first train is

 54 km/hr
 50 km/hr
 52 km/hr
 51 km/hr

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Speed of second train
= 43.2 kmph= 43.2 × 5 m/sec. 18
or 12 m/sec.Let the speed of first train be x m per second, then150 + 120 = 10 x + 12
⇒ 27 = + x 12
⇒ x = 15 m/s= 15 × 18 kmph = 54 kmph 5 Correct Option: A
Speed of second train
= 43.2 kmph= 43.2 × 5 m/sec. 18
or 12 m/sec.Let the speed of first train be x m per second, then150 + 120 = 10 x + 12
⇒ 27 = + x 12
⇒ x = 15 m/s= 15 × 18 kmph = 54 kmph 5
 Two trains of length 137 metre and 163 metre are running with speed of 42 km/hr and 48 km/hr respectively towards each other on papallel tracks. In how many seconds will they cross each other?

 30 sec
 24 sec
 12 sec
 10 sec

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Relative speed = 42 + 48 = 90 kmph
= 90 × 5 m/s = 25 m/s 18
Sum of the length of both trains
= 137 + 163 = 300 metres∴ Required time = 300 = 12 seconds. 25 Correct Option: C
Relative speed = 42 + 48 = 90 kmph
= 90 × 5 m/s = 25 m/s 18
Sum of the length of both trains
= 137 + 163 = 300 metres∴ Required time = 300 = 12 seconds. 25