Question

a train, 218 m long, travelling at 63kmph can cross a platform in 32 seconds. if a man can cross the same platform in 3 minutes, what is the speed of the man( in m/sec)?​

Answer 1

Given:

A train, 218 m long travelling at 63 kmph can go over a platform in 32 seconds.

A man can go over the same platform in 3 minutes

To find:

What is the speed of the man (in m/sec)?​

Solution:

The length of the train = 218 m

The speed of the train = 63 km/hr = $63 \times \frac{5}{18} \:m/s = 17.5 \:m/s$

The time taken to go over the platform = 32 seconds

Let "L" meter represents the length of the platform.

Therefore,

$Speed \:of\:train = \frac{[Length\:of\:the \:train] + [Length\:of\:the \:platform]}{Time\:taken\: for\:crossing}$

$\implies 17.5 = \frac{218 + L }{32}$

$\implies 560 = 218 + L$

$\implies L = 560 - 218$

$\implies \bold{L = 342\:m}$

Let "S" m/s be the speed of the man.

The man takes 3 minutes = 3 × 60 s = 180 s to go over the same platform of length 342 m

We know,

$\boxed{\bold{Speed = \frac{Distance }{Time} }}$

Therefore, we get

$S = \frac{342}{180} = 1.9 \:m/s$

Thus, the speed of the man is → 1.9 m/s.

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