Question

220 metre long train is running at a speed of 54 km per hour in what time will it pass a man who is moving in the opposite direction of the train at a speed of 12 kilometre per hour ​

Answer 1

Time to pass a man who is moving in the opposite direction of the train is 12 second.

Step-by-step explanation:

1. Given data

  Length of train = 220 m          ...1)

  Speed of train $\mathbf{=54\left ( \frac{km}{h} \right )}$

  Speed of man $\mathbf{=12\left ( \frac{km}{h} \right )}$

2. As man and train is moving in opposite direction. So

   Relative speed of train with respect to man$\mathbf{=Train Speed+ Man Speed}$

   Relative speed $\mathbf{(V_{rel})=54+12=66\left ( \frac{km}{h} \right )}$

   In terms of metre per second, we can write this

   $\mathbf{V_{rel}=54+12=66\left ( \frac{km}{h} \right )=66\times \frac{1000}{3600}\left ( \frac{m}{s} \right )}$

   On solving

   $\mathbf{(V_{rel})= \frac{55}{3}\left ( \frac{m}{s} \right )}$          ...2)

3. From speed, distance and time formula

   $\mathbf{Time=\frac{Distance}{Speed}}$           ...3)

   In equation 3)

   Distance = Length of train = 220 m

   Speed = Relative speed $\mathbf{=\frac{55}{3}\left ( \frac{m}{s} \right )}$

4. Now from equation 1), equation 2) and equation 3)

   Time to pass man by train $\mathbf{=\frac{220}{\frac{55}{3}}=\frac{220\times 3}{55}=12 second}$

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