Question

Two cars, A and B start from pretoria to polokwane respectively simultaneously and travel towards each other at constant speeds along the route.After meeting at a point between pretoria and polokwane,the two cars proceed to their respective destinations of polokwane and pretoria.car A reaches polokwane 40 minutes after the two cars have met and car B reaches pretoria 90 minutes after they have met.How long did it take car A to cover the distance between pretoria and polokwane? (5 marks)

Answer 1

Let the distance of polokwane from pretoria be x
Let the cars meet at p < x
If car A has speed a and B has speed b, then

p/a = (x-p)/b
(x-p)/a = 2/3
p/b = 3/2

The solution is not unique. We get

p = (3/5) x
a = p
b = 2/3 p

It takes A 100 minutes

With a little checking, you can see that it does not matter what the actual distance and speeds are, as long as they meet 3/5 of the way from Pretoria to Polokwane.

It then takes A 2/3 hr to cover 2/5 the distance. Thus, it takes 5/3 hr = 100 minutes to cover the whole distance.