Question

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

Answer 1

Let the speed of train be x km/h.

Distance = 300 km

So, time = $\frac{300}{x}$

When speed is 5 km/h more, time taken = $\frac{300}{x+5}$

According to the given information, $\frac{300}{x}-\frac{300}{x+5}=2$

$\Rightarrow 300(x+5)-300x=2x(x+5)\Rightarrow 2x^2+10x-1500=0\Rightarrow x^2+5x-750=0$

$\Rightarrow x^2+30x-25x-750\Rightarrow x(x+30)-25(x+30)=0\Rightarrow x=-30,25$

Discarding the negative value, speed of the train = 25 kmph.