3. A fast train takes one hour less than a slow train for a journey of km. If the speed of the slow train is km/hr less than that of the fast train, find the speed of the two trains.

Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring.

Solution:

Let’s consider the speed of the fast train as x km/hr

Then, the speed of the slow train will be km/hr

Using, speed = distance/ time

Time taken by the fast train to cover km  hr

And, time taken by the slow train to cover km hr

Given, that the difference in the times is hour.

This can be expressed as below:

[by factorisation method]

As, the speed of train can never be negative we neglect

Thus, speed of the fast train is km/hr

And the speed of slow train km/hr