Question

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/ hour, it takes 2 hours less in the journey. Find the original speed of the train.

Answer 1

Let original speed of train = x km/hr
Increased speed of train = (x + 5) km/hr
Distance = 300 km
According to the question,
$\frac{300}{x}-\frac{300}{x+5}=2$
$\frac{300(x+5-x)}{\left(x\right)(x+5)}=2$
$1500=2(x^2+5x)$
$1500=2x^2+10x$
$2x^2+10x-1500=0$
$x^2+5x-750=0$
$x^2+30x-25x-750=0$
$x(x+30)-25(x+30)=0$
$(x+30)(x-25)=0$
Either x + 30 = 0 or x - 25 = 0
$\Rightarrow$ x = -30 (Rejected), so x = 25
Original speed of train is 25 km/hr.