If two trains or two bodies are moving in the same direction at u m/s and v m/s, then their
R elative Speed = (u - v) m / s
Distance covered = Sum of length of two trains
Time = Distance / Speed
Time = Sum of length of two trains / (u - v)
To convert minutes into hour, we should divide the given minutes by 60.
Example 1 :
A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Solution :
The train and a man are travelling in the same direction.
So,
Relative speed = Speed of the train - Speed of the man
= 68 - 8
= 60 km/hr
Converting the speed from km/hr to m/sec
= 60 ⋅ (5/18)
= 50/3
Since the train crosses the man, the distance covered by the train is 150 m (the length of the train).
Time = 150 / (50/3)
= 150 ⋅ (3/50)
= 9 seconds
Example 2 :
Two trains 100 meters and 120 meters long are running in the same direction with speeds of 72 km/hr and 54 km/hr. In how much time will the first train cross the second ?
Solution :
Since both are moving objects and the total distance covered
= 100 + 120
= 220 meters
Relative speed = 72 - 54
= 18
Relative speed in m/sec = 18 ⋅ (5/18)
= 5 m/sec
Time = Distance / Speed
= 220 / 5
= 44 seconds
Hence the first train is taking 44 seconds to cross the second train.
Example 3 :
A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and length of the platform.
Solution :
Let x and y be the length of the train and length of platform.
Distance covered by the train while crossing the platform
= x + y
Time taken by the train to cross the platform = 20 sec
Speed of the train and = 54 km/hr
54 km/hr = 54 ⋅ (5/18)
= 15 m/sec
Time taken by the train to cross the platform is
Time = Distance / Speed
20 = (x + y) / 15 -----(1)
Time taken by the train to cross the platform = 12 sec
Speed of the man = 6 km/hr
Relative speed = 54 - 6
= 48 kmph
48 km/hr = 48 ⋅ (5/18)
= (40/3) m/sec
Time taken by the train to cross a man is
Time = Distance / Speed
12 = x / (40/3)
x = 160
By applying the value of x in (1), we get
20 = (160 + y) / 15
y = 300 - 160
y = 140 m
Hence the length of the train and the length of the platform are 160 m and 140 m respectively.
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