@quacker88 Hi! Thanks for the helpful explanation because I had the same question victorioussheep did. It's just when I tried to solve the problem you gave, I got the answer B/(B-A).(1/A-1/B)t=1 Simplifying (1/A-1/B), I get (B-A/AB)t=1 and so t= AB/B-A. t is the time it takes for the first runner to catch up with the second runner. So the number of laps the first runner runs is AB/B-A divided by A which is B/B-A.
Also, I think how Prof. Loh got A/A-B was by solving for the number of laps the trainer or the second runner was running.
I don't know if this is correct, but I hope you can look over my work. Thanks!