A train $100 m$ long takes $6 s e c o n d s$ to cross a man walking at $5 k m / h$ in a direction opposite to that of the train. The speed of the train is?

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Solution

Finding the speed of the train.
Given that, the length of a train $= 100 m = \frac{100}{1000} = \frac{1}{10} k m [A s 1 m = \frac{1}{1000} k m]$
Time taken by train to cross the man $= 6 s e c = \frac{6}{3600} = \frac{1}{600} h [A s 1 h = \frac{1}{3600} s e c]$
Let the speed of the train $= x k m / h$
Since train is crossing the man walking opposite to the direction of train whose speed is $5 k m / h$
Therefore relative speed $= (x + 5) k m / h$
As we know,
$d i s \tan c e = s p e e d x t i m e \Rightarrow \frac{1}{10} = (x + 5) x \frac{1}{600} \Rightarrow \frac{600}{10} = (x + 5) \Rightarrow 60 = x + 5 \Rightarrow x = 55 k m / h$
Hence, the speed of the train is $55 k m / h$ .

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A train 100m long takes 6seconds to cross a man walking at 5km/hin a direction opposite to that of the train. The speed of the train is?

A train $100 m$ long takes $6 s e c o n d s$ to cross a man walking at $5 k m / h$ in a direction opposite to that of the train. The speed of the train is?