Question

A passenger train takes two hours more for a journey of $300$km if its speed is decreased by $5$km/hr from its usual speed. Find the usual speed of the train.

Answer 1

Let the normal speed of the train be $s$ km/hr

We know that $\left(speed\right)\left(time\right)=distance$

Usual time taken by train $=\frac{300}{s}$

Time taken when speed is reduced is $=\frac{300}{s-5}$

According to the question

$\frac{300}{s}+2=\frac{300}{s-5}$

$\Rightarrow \frac{300}{s}-\frac{300}{s-5}=-2$

$\Rightarrow 300(\frac{1}{s}-\frac{1}{s-5})=-2$

$\Rightarrow 150\left(\frac{s-5+s}{s(s-5)}\right)=-1$

$\Rightarrow s^2-5s-750=0$

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

$\Rightarrow (s-30)(s+25)=0$

$s=30$ km/hr is the usual speed.