Question

A train travels a distance of $300km$ at constant speed. If the speed of the train is increased by $5km$ an hour, the journey would have taken $2$ hours less. find the original speed of the train.

Answer 1

Let $x$ km/hr be the constant speed of the train,

Then Time taken to cover $300km=\frac{300}{x}hrs$

Time taken to cover $300km$ when the speed is increased by $5km/hr=\frac{300}{x+5}hours$

It is given that the time to cover $300km$ is reduced by $2$ hours

$\therefore \frac{300}{x}-\frac{300}{x+5}=2$

$\Rightarrow \frac{300(x+5)-300x}{x(x+5)}=2\Rightarrow 2x^2+10x=1500$

$\Rightarrow x^2+5x-750=0\Rightarrow x^2+30x-25x-750=0$

$\Rightarrow (x+30)(x-25)=0\Rightarrow x=25orx=-30$

But $x$ cannot be negative. Therefore $x=25$

Hence, the original speed of the train is $25km/hr$