Question

A person travelled a distance of 200 kilometre between two cities by a car covering the first quarter of the journey at a constant speed of 40 km/h and he remaining three quarters at a constant speed of x km/h. if the average speed of the person for the entire journey was 53.33 km/h what is the value of x?

Answer 1

First quarter of the journey = ¼ x 200 = 50 km

Time taken = 50/40 = 1.25 hours

Remaining distance = 200 – 50 = 150 km


Time taken = 150/x

Total time = 1.25 + 150/x

Average speed = Total distance/Total time

                  53.33 = 200 / (1.25 + 150/x)

1.25 + 150/x = 200/53.33

150/x = 200/53.33 – 1.25


150/x = 2.5


x = 150/2.5


x = 60


x = 60 km/h

Answer 2

First quarter of the journey = ¼ x 200 = 50 km

Time taken = 50/40 = 1.25 hours

Remaining distance = 200 – 50 = 150 km

The total time would be 200/53.33 = 3.75 hours

Therefore 3.75-1.25 = 2.50 hours = 150 mins

It covers remaining 150 k.m in 150 mins, that means 60 k.m in 60 mins