A 242 m long train crosses a man walking at a speed of 9.5 km/h in the opposite direction in 24 seconds. What is the speed (in km/h) of the train ?

Correct option is B

Given:

Length of the train = 242 m
Speed of the man = 9.5 km/h
Time taken to cross the man = 24 seconds

Formula Used:

When objects move in opposite directions, their relative speed is the sum of their individual speeds.

Relative Speed = $$\frac{\text{Distance }}{\text{ Time}}$$​​

Solutions:

Let the speed of the train be $$S_{train}$$​ km/h.

Relative speed $$S_{relative} = S_{train} + S_{man}$$​ (since they are moving in opposite directions)

​$$S_{relative} = (S_{train}$$​ + 9.5) km/h.

Relative Speed (m/s) = $$\frac{\text{Length of train (m) }}{\text{ Time (s)}}$$​​

$$S_{relative}$$​ =$$\frac{242 m}{ 24 s}$$​​

​$$S_{\text{relative (km/h)}} =\frac{ 121 }{ 12} × \frac{18}5$$ = 36.3 km/h

We know that:
​$$S_{\text{relative }}= S_{\text{train}} + S_{\text{man}}$$​​

36.3 = $$S_{\text{train}}$$​ + 9.5

​$$S_{\text{train}}$$​ = 36.3 - 9.5

​$$S_{\text{train}}$$​ = 26.8 km/h

The speed of the train is 26.8 km/h.