Two cars leave simultaneously from points X and Y on the same road but in opposite directions. Their speeds are constant, and in the ratio 5 to 4 with the car leaving at X being the faster of the two.

The cars travel to and fro between X and Y. They meet for the second time at the 145th milestone and for the third time at the 201st milestone.

Let the milestones at X and Y show x and y, so that the distance from X to Y is y – x miles. At any stage, the distances travelled by the cars must be in the ratio 5:4. Thus, at the 2^{nd} and 3^{rd} meetings: