Question

An express train makes a run of 240 km at a certain speed. Another train , whose speed is 12 km/hr less than the first train takes an hour longer to make the same trip . Find the speed of the express train in km/hr.

Answer 1

Let the speed of express train be x km/h Then the speed of ordinary train will be (x-12) km/h.

Time taken by express train =$\frac{240}{x}$
Time taken by ordinary trian=$\frac{240}{x-12}$
According to the given condition:
$\frac{240}{x-12}-\frac{240}{x}=1$
$\Rightarrow 240\left(\frac{x-(x-12)}{x(x-12)}\right)=1$
$\Rightarrow 240\times \frac{x-x+12}{x(x-12)}=1$
$\Rightarrow 240\times \frac{12}{x(x-12)}=1$
$\Rightarrow 2880=x^2-12x$
$\Rightarrow x^2-12x-2880=0$
$\Rightarrow x^2-60x+48x-2880=0$
$\Rightarrow x(x-60)+48(x-60)=0$
$\Rightarrow (x-60)(x+48)=0$
$\therefore x=60,-48$
Since, speed can't be a negative quantity.
So, the speed of the express train is 60 km/h.