Question

An express train takes $1$ hour less than a passenger train to travel $132km$ between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is $11km/hr$ more than that of the passenger train, find the average speed of the two trains.

Answer 1

Let $x$ km per hour be the average speed of the passenger train, then the average speed of the express train will be $\left(x+11\right)$ km per hour.

The time taken by the passenger train is $\frac{132}{x}$ hour and the time taken by the express train is $\frac{132}{\left(x+11\right)}$ hour. So,

$\frac{132}{x+11}=\frac{132}{x}+1$

$x^2+11x-1452=0$

$x^2+44x-33x-1452=0$

$\left(x-33\right)\left(x+44\right)=0$

$x=33,x=-44$

The speed cannot be negative, so the speed of the passenger train is 33 km per hour and the speed of the express train is $33+11=44$ km per hour.