Question

A policeman is standing on a railway bridge which is $60$ meters long. He finds that a train crosses the bridge in $4\frac{1}{2}$ seconds but himself in $2$ seconds. What is the length of the train and its speed

Answer 1

Let $x$ and $v$ be the length and speed of train.

Length of platform $=60m$

Time taken by the train to cross the bridge $=4\frac{1}{2}=\frac{9}{2}s$

Time taken by the train to cross the policeman $=2s$

Now,

When the train crosses policeman-

$t=\frac{x}{s}$

$\Rightarrow s=\frac{x}{2}$

When the train crosses platform,

$t=\frac{x+60}{s}$

$\frac{9}{2}=\frac{x+60}{\frac{x}{2}}$

$\Rightarrow \frac{9}{2}\times \frac{x}{2}=x+60$

$9x=4x+240$

$\Rightarrow 9x-4x=240$

$\Rightarrow x=\frac{240}{5}=48m$

Hence the length of train is $48m$.