Question

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

(a) \(2\frac37\) seconds

(b) \(3\frac37\) seconds 

(c) \(4\frac37\) seconds 

(d) \(5\frac37\) seconds

Answer 1

(b)   \(3\frac37\) seconds 

Let the length of 1st train = length of the 2nd train = x metres

Then, speed of the 1st train = \(\frac{x}{3}\) m/s

Speed of the 2nd train = \(\frac{x}{4}\) m/s

Since both the trains are moving in opposite directions, their relative speed = \(\bigg(\frac{x}{3} + \frac{x}{4}\bigg)=\frac{7x}{12}\) m/s

∴ Time taken to pass each other = \(\frac{\text{Distance to be covered}}{\text{Relative speed}}\)

= \(\frac{x+x}{\frac{7x}{12}}=\frac{2x\times12}{7x}=\frac{24}{7}\) seconds

=   \(3\frac37\) seconds.