#### Question

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 1 1 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.

#### Solution

Let the arrange speed of express train be denoted by x km/hr

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

⇒ Average speed of passenger train = (x - 11)km/hr

Total distance travelled by the train = 132 km

We know that,

`"Time taken to travel" = "Distance travelled"/"Average speed"=132/x hr`

`rArr"Time taken by express train" ="Distance travelled"/"Average speed of express train"=132/(x-11) hr`

Given that time taken by express train is 1 hour less than that of passenger train.

⇒ Time taken by passenger train - Time taken by express train = 1 hour

`rArr132/(x-11)-132/x=1`

`rArr132(1/(x-11)-1/x)=1`

`rArr132((x-(x-11))/(x(x-11)))=1`

⇒ 132(x - x + 11) = x(x - 11)

⇒ 132(11) = x^{2} - 11x

⇒ 1452 = x^{2} - 11x

⇒ x^{2} - 11x - 1452 = 0

The required quadratic is x^{2} - 11x - 1452 = 0