what is the ratio of their speed?

Question

Jonathan and Cindy run on a circular track where AB is the diameter of the track, as shown below. If Jonathan and Cindy run towards each other at the same time from Point A and Point B respectively, it will take them 40 seconds before they meet. If they start running at the same time but in the same direction, it will take Jonathan 280 seconds to catch up with Cindy. What is the ration of their speeds?

Answer 1

We assume they are on a line, because the circle makes no difference.

Let $s$ be the change in mutual distance.

If they run towards each other, their velocities add up $s = (v_1 + v_2) \times 40$

If one is chasing the other, they subtract $s = (v_1 - v_2) \times 280$

So

$(v_1 - v_2) \times 280 = (v_1 + v_2) \times 40$

$220 v_1 = 320 v_2$

$v_1/v_2 = 320/220 \approx 1.5$