Question

A man standing on a platform 225m long notices that a train travelling at uniform speed passes him in 6sec and passes by the platform in 21sec. Find (I) the length of the train and (ii) the speed of the train
SOLVE IT WITH FULL EXPLANATION​

Answer 1

Answer:

i) The length of the train is 90 m

ii) The speed of the train is $15\ m/s$

Step-by-step explanation:

Given that the length of the platform is 225 meters and the train passes the platform in 21 seconds.

Let $x$ be the length of the train.

Since the train is traveling at a uniform speed, we can take the speed as $s$.

Since the train passes the man in 6 seconds, it travels the distance equal to the length of the train in 6 seconds. So,

$\implies s = \dfrac{x}{6} \\\\\implies x= 6s$

Also, the train travels the distance which is equal to the length of the train and the platform in 21 seconds. So,

$\implies s=\dfrac{225+x}{21} \\\\\implies 225+x=21s\\\\\implies x=21s-225$

Equating the equations, we get

$\implies 21s-225=6s\\\\\implies 21s-6s=225\\\\\implies 15s=225\\\\\implies s=\dfrac{225}{15}=15 \ m/s$

So the speed of the train is $15\ m/s$. Thus the train has a length,

$x=6\times 15=90\ m$.