An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.

Given:

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore.

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

To do:

We have to form the quadratic equation to find the average speed of the express train.

Solution:

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

This implies, the average speed of the passenger train is $x-11$ km/hr.

Time taken by the express train to cover 132 km$=\frac{132}{x}$ hours.

Time taken by the passenger train to cover 132 km$=\frac{132}{x-11}$ hours.

Therefore,

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

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

$132x-132x+132(11)=1(x^2-11x)$

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

The required equation is $x^2-11x-1452=0$.

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