Question

A fast train takes $3$ hours less than a slow train for a journeyof $600Km$. If the speed of the slow train is $10Kmh{r}^{-1}$ less than the faster train, find the speeds of the two trains.

Answer 1

Let speed of faster train be x km/hr

speed of slow train = (x-10) km/hr.

Given faster train takes 3 hrs less to travel 600km

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

(time taken by faster train) (time taken by slower train)

$600[\frac{1}{x-10}-\frac{1}{x}]=3$

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

$\frac{10}{x(x-10)}=\frac{3}{600}=\frac{1}{200}$

$2000=x(x-10)$

$50\times 40=x(x-10)$

$x=50km/hr$

$\therefore$ speeds of train are 50 km/hrs and 40 km/hrs