Mr. Njinga cycled a distance of 42km from his village. On his return journey he increased his speed by 2km/h and took half an hour less. Calculate the average speed on the journey from his village.

Answer 1

speed on first part ---- x km/h
speed on return trip -- x+2 km/h

time on first trip = 42/x
time on 2nd trip = 42/(x+2)

42/x - 42/(x+2) =1/2
multiply each term by 2x(x+2)

84(x+2) - 84x = x(x+2)
84x + 168 - 84x = x^2 + 2x

x^2 + 2x - 168 = 0
(x-12)(x+14)=0
x = 12 or x =-14, let's reject the x = -14

x = 12 km/h

find each individual times by subbing this back into my time definitions.
average speed = 84/(sum of the above times)
= ....

Answer 2

Thank you very much