Question

A fast train takes $3$ hours less than a slow train for a journey of $600km$. If the speed of the slow train is $10km/hr$ less than that of the fast train, find the speeds of the two trains.

Answer 1

Let the speed of the slow train be $x$ km/hr. Then, the speed of the fast train is $(x+10)$ km/hr

Time taken by the slow train to cover $600km=\frac{600}{x}hr$

Time taken by the fast train to cover $600km=\frac{600}{x+10}hr$
$\therefore \frac{600}{x}-\frac{600}{x+10}=3$

$\Rightarrow \frac{600(x+10)-600x}{x(x+10)}=3$

$3=\frac{6000}{x^2+10x}$

$\Rightarrow 3(x^2+10x)=6000$

$\Rightarrow x^2+10x-2000=0\Rightarrow x^2+50x-40x-2000=0$

$\Rightarrow (x+50)(x-4)=0$

$\Rightarrow x=-50orx=40\Rightarrow x=40$

Hence, the speeds of two trains are $40$ km.hr and $50$ km/hr