Question

A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train

Answer 1

Let the usual speed of the train be $=x$ km\hr

Total distance$=300$km

$\therefore$ Time taken$=\frac{300}{x}$hrs. ............$\left(1\right)$

New speed of the train$=(x+5)$km\hr

Time taken$=\frac{300}{(x+5)}$hrs. ............$\left(2\right)$

According to given condition,

$\frac{300}{x}-\frac{300}{x+5}=2$ from $\left(1\right)$ and $\left(2\right)$

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

$\Rightarrow 1500=2x^2+10x$

$\Rightarrow 2x^2+10x-1500=0$

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

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

$\Rightarrow x+30=0$ or $x-25=0$

$x=-30$(rejected) $\therefore x=25$

$\therefore$ usual speed of the train$=25$km\hr.