Question

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds and crosses the man in 8 seconds. Find the length of the train. [ 3 marks ]

Answer 1

Let length of train = x m

$\therefore$ Distance covered to cross the bridge

= (180 + x)m
[ 0.5 marks ]
Distance covered to cross the man = x m

$\begin{array}{ccc}Distancecovered& 180+x& x\\ Timetaken& 20& 8\end{array}$

$\because$ speed is constant

$\therefore$ Distance covered is directly proportional to the time taken.
[ 1 mark ]
$\Rightarrow \frac{180+x}{20}=\frac{x}{8}$

$\Rightarrow \frac{180+x}{20}=\frac{x}{8}$
[ 0.5 marks ]
$\Rightarrow 8(180+x)=20x$

$\Rightarrow 1440+8x=20x$

$\Rightarrow 1440=20x-8x$

$\Rightarrow 1440=12x$

$\Rightarrow \frac{1440}{12}=x$

$\Rightarrow 120=x$

Hence the length of the train

$=120m$
[ 1 mark ]