A train travels 180 km at a uniform speed. If the speed had been 9km/hour more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Given: Distance travelled by the train = 180 km.

Let the speed of train = x km/hr

Time taken by train to cover 180 km with (x) km/hr speed =

= (180/x ) hr

Let the increased speed of the train = (x + 9) km/hr

Time taken by train to cover 180 km with (x + 9) km/hr speed =

= (180/x + 9) hr

Now, given that the if the speed be (x + 9) km/hr, then the train will take 1 hour less to travel the same distance.

So, according to the question,

= 1

Now, solving it further as follows:

= 1

⇒ 180x - 180(x + 9) = x (x + 9)

⇒ 180x - 180x - 1620 = x² + 9x

⇒ x ² + 9x - 1620 = 0

⇒ x ² - 36x + 45x - 1620 = 0

⇒ x (x - 36) + 45(x – 36) = 0

⇒ (x - 36)(x + 45) = 0

⇒ x = 36 or -45

But, speed can’t be negative, therefore speed = 36 km/hr.