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

Question:

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

Solution:

Now let us assume that the speed of the express train be ‘x’ km/hr. Therefore according to the question speed of the passenger train will be ‘−11’ km/hr. Now we know that the total distance travelled by both the trains was 132 km.

We also know that

So the time taken by express train would be $\left(\frac{132}{x}\right)$ hr and the time taken by the passenger train would be $\left(\frac{132}{x-11}\right)$ hr. Now, we also know that the express train took 1 hr less than the passenger train to travel the whole distance.

Therefore, we have

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

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

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

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

Therefore, this is the required equation.