2. A train, traveling at a uniform speed for km, would have taken minutes less to travel the same distance if its speed were km/hr more. Find the original speed of the train.

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

Solution:

Let the original speed of train be km/hr

When increased by , speed of the train km/hr

Using, speed = distance/ time

Time taken by the train for original uniform speed to cover km hr.

And, time taken by the train for increased speed to cover km hr.

Given, that the difference in the times is mins. ⇒ hour

This can be expressed as below:

[by factorisation method]

or

Since, the speed of the train can never be negative is not considered.

Therefore, the original speed of train is km/hr.