Question

The distance between two places is 900 km. An ordinary express train takes 5 hours more than a superfast express train to cover this distance. If the speed of the superfast express train is 15 km/hr more than that of the ordinary express train, find the speed of the trains.

Answer 1

Let speed of ordinary train=x

then speed of superfast train=x+15

Time required by ordinary train=900/x

Time required by ordinary train=900/(x+15)

Difference in time=5hr

So,

$\begin{array}{c}\frac{900}{x}-\frac{900}{x+15}=5\\ \frac{1}{x}-\frac{1}{x+15}=\frac{5}{900}\\ \frac{x+15-x}{x\left(x+15\right)}=\frac{1}{180}\\ 180\times 15=x^2+15x\\ x^2+15x-2700=0\\ \left(x+60\right)\left(x-45\right)=0\\ x=-60,45\end{array}$

As velocity cannot be negative.

So, x=45

and x+15=45+15

=60

Thus speed will be 45Kmph and 60 Km/hr