A motorcyclist and a cyclist left points A and B at the same time to meet each other.

A motorcyclist and a cyclist left points A and B at the same time to meet each other. How long did the cyclist take all the way if it took the motorcyclist 24 minutes, and their meeting took place 18 minutes after leaving?

Suppose the rider’s speed is x m / min and the cyclist’s speed is y m / min.

Then, according to the condition of the problem, we can compose the following equation:

24 * x = 18 * (x + y),

24 * x = 18 * x + 18 * y,

24 * x – 18 * x = 18 * y,

6 * x = 18 * y,

x = 3 * y.

We got that the speed of a cyclist is 3 times less than the speed of a motorcyclist, which means that the cyclist will spend 3 times more time on the path from A to B, that is

24 * 3 = 72 (min) = 1 hour 12 minutes.

Answer: 1 hour 12 minutes.