Question

The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at the speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?

Answer 1

Let the ongoing speed of person be x km/hr,

Then, the returning speed of the person is = (x + 10) km/hr (from the question)

Using, speed = distance/ time

Time taken by the person in going direction to cover 150 km = 150/x hr

And, time taken by the person in returning direction to cover 150 km = 150/(x + 10)hr

Given, that the difference in the times is 2.5 hour ⇒ 5/2 hours

This can be expressed as below:

3000 = 5x² + 50x

5x² + 50x – 3000 = 0

5(x² + 10x – 600) = 0

x² + 10x – 600 = 0

x² – 20x + 30x – 600 = 0 [by factorisation method]

x(x – 20) + 30(x – 20) = 0

(x – 20)(x + 30) = 0

x = 20  or x = -30(neglected) As the speed of train can never be negative.

Thus, x = 20 Then, (x + 10) (20 + 10) = 30

Therefore, the ongoing speed of person is 20km/hr.

And the returning speed of the person is 30 km/hr.