Question

While traveling from A to B, the average speed of the passenger train is 11km/hr less than the average speed of the express train. If the express train reaches 1 hour earlier than the passenger train, find the average speed of both the trains.

Answer 1

Let the average speed of passenger train be x km/h.
Average speed of express train =(x+11)km/h
It is given that the time taken by the express train to cover 132 km is 1 hour less than the passenger train to cover the same distance.
$\therefore \frac{132}{x}-\frac{132}{x+11}=1\Rightarrow 132\left[\frac{x+11-x}{x(x+11)}\right]=1\Rightarrow \frac{132\times 11}{x(x+11)}=1\Rightarrow 132\times 11=x(x+11)\Rightarrow x^2+11x-1452=0\Rightarrow x^2+44x-33x-1452=0\Rightarrow x(x+44)-33(x+44)=0\Rightarrow (x+44)(x-33)=0\Rightarrow x=-44,33$
Speed cannot be negative
Therefore, the speed of the passenger train will be 33 km/h and thus, the speed of the express train will be 33 + 11 = 44 km/h.