Question

37.

An express train travelled at a certain average speed from Town X to Town Y which was
150 km away. It then continued its journey to Town Z at an average speed 20 km/h faster than
its initial average speed. Town Ywas 200 km from Town Z. If it took the same time to travel for
both parts of the journey, what was the train's average speed for the first part of the journey?​

Answer 1

60 km/hr

Explanation:

Let the speed at the initial average speed from Town X to Town Y be a.

We are told that it journeyed to Town Z at an average speed 20 km/h faster than its initial average speed. Thus, its average speed here is (a + 20) km/hr.

Town Y was 200 km from Town Z.

Thus, time spent here is;

t_2 = 200/(a + 20)

Time from X to Y is; t_1 = 150/a

We are told that it took the same time to travel for both parts of the journey.

Thus; t_1 = t_2

150/a = 200/(a + 20)

Cross multiply to get;

150(a + 20) = 200a

150a + 3000 = 200a

200a - 150a = 3000

50a = 3000

a = 3000/50

a = 60 km/hr