Question

A train moves past a telegraph post and a bridge $264$ m long in $8$ seconds and $20$ seconds respectively. what is the speed of the train?

• A. $69.5$ km/hr
• B. $70$ km/hr
• C. $79$ km/hr
• D. $79.2$ km/hr

Answer 1

Answer: (D)

$79.2$ km/hr

Let the length and speed of train be $L,M$ and $S$m/s.

When train passes through telegraph pole in $8$ sec.

$L=S\times 8$ [Formula: Distance=speed $\times$ time

$⟹S=\frac{L}{8}$

When train passed through bridge of $264$ in $20$sec

$(264+L)=S\times 20\Rightarrow 264+L=\frac{L}{8}\times 20\Rightarrow 2(264+L)=5L\Rightarrow 528+2L=5L\Rightarrow 5L-2L=528\Rightarrow 3L=528\Rightarrow L=\frac{528}{3}m$

Speed of train =$S=\frac{L}{8}=\frac{528}{3\times 8}m/s=22m/s$

$\Rightarrow S=22\times \frac{18}{5}km/hr=\frac{396}{5}km/hr\Rightarrow S=79.2km/hr$