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

Given:

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations).

The average speed of the express train is 11 km/hr more than that of the passenger train.

To do:

We have to find the average speed of the two trains.

Solution:

Let the average speed of the passenger train be $x$ km/hr.

This implies,

The average speed of the express train$=x+11$ km/hr.

Time taken by the passenger train to travel 132 km $=\frac{132}{x}$ hours

Time taken by the express train to travel 132 km $=\frac{132}{x+11}$ hours

According to the question,

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

$\frac{132(x+11)-132(x)}{(x)(x+11)}=1$

$\frac{132(x+11-x)}{x^2+11x}=1$

$(132)(11)=1(x^2+11x)$ (On cross multiplication)

$1452=x^2+11x$

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

Solving for $x$ by factorization method, we get,

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

$x(x+44)-33(x+44)=0$

$(x+44)(x-33)=0$

$x+44=0$ or $x-33=0$

$x=-44$ or $x=33$

Speed cannot be negative. Therefore, the value of $x$ is $33$ km/hr.

$x+11=33+11=44$ km/hr

The speed of the passenger train is $33$ km/hr and the speed of the express train is $44$ km/hr.

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