A wants to catch up with B, that is, A has to run one more lap than B. It takes X minutes to catch up for the first time without rest.

According to the meaning of the question:

120x- 100x=500

The solution is x=25 (minutes).

A * * * escaped: 120*25=3000 (m)

* * * Rest: 3000/200= 15 (minutes)

Then 15+25=40 (minutes) is needed.