A train can cross a platform of equal length in 5 minutes. It can cross a man running in the direction of the train with the speed of 2m/s in 7 minutes. Find the speed of the train(in km/h).
Answers
Answer:
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Speed of train = 11.2 km/h
Step-by-step explanation:
Given :
Length of train = length of platform = x m (let)
Time to cross the platform = 5 minutes.
Speed of the running man = 2m/s
Time to cross the man = 7 minutes.
To find :
Speed of the train (in km/h)
Solution :
When train crosses the platform, distance covered by the train = length of the train + length of the platform = x + x = 2x.
Time taken = 5 minutes = 300 seconds.
Speed of the train = Distance/Time.
= (2x/300) m/s
= (x/150) m/s
Relative speed of train (with respect to man, when man is assumed to be stationary )
= (x/150 - 2) m/s
Time to cross the man = 7 minutes
= 420 seconds.
Distance travelled by train to cross the man
= it's own length x m.
Distance = Speed × time
x = (x/150 - 2) × 420
x = 420x/150 - 840
x = 14x/5 - 840
840 = 14x/5 - x
9x/5 = 840
x = 840 × (5/9)
x = 1400/3
speed of train = x/150
= (1400/3) ÷ 150
= 28/9 m/s
Speed in km/h = (28/9) × (18/5)
= 56/5 km/h
= 11.2 km/h
Hence, the speed of the train = 11.2 km/h