Question

A train passes $300m$ long platform in $30s$ and it crosses a signal on the station in $12s$. Find:
the length of the train

Answer 1

Let $l$ and $s$ be the length of train and speed of train respectively.

now,

Length of platform $=300m$

Time taken by the train to cross the signal $=\frac{\text{length of train}}{\text{Speed of train}}$

$\Rightarrow \frac{l}{s}=12$

$\Rightarrow l=12s.....\left(1\right)$

Now,

Time taken by the train to cross the platform $=\frac{\text{length of train}+\text{length of platform}}{\text{speed of train}}$

$\Rightarrow 30=\frac{l+300}{s}$

$\Rightarrow 30s=12s+300\left(\text{From}\left(1\right)\right)$

$\Rightarrow 30s-12s=300$

$\Rightarrow s=\frac{300}{18}=\frac{50}{3}m/s$

Substituting the value of $s$ in equation $\left(1\right)$, we have

$l=12\times \frac{50}{3}=50\times 4=200m$

Hence the length of the train is $200m$.