Question

A train travelling at $40kmh$ crosses a signal post in $30sec$. It passes a platform in $45sec$. Find the length of the platform.

Answer 1

Let $d$ and $x$ be the length of train and platform respectivey.

Speed of train $=40km/hr=40\times \frac{5}{18}=\frac{100}{9}$

Therefore,

Time taken by the train to pass the signal $=\frac{d}{\left(\frac{100}{9}\right)}$

$\Rightarrow d=30\times \frac{100}{9}=\frac{1000}{3}m$

Now,

Time taken by the train to pass the platform $=\frac{\frac{1000}{3}+x}{\frac{100}{9}}$

$\frac{1000}{3}+x=\frac{100}{9}\times 45$

$\Rightarrow x=500-\frac{1000}{3}=\frac{500}{3}m$