Statement
Sussi Paul's comment is a good solution.
The idea is to tell us about the relative speeds of both, and we ask that we place the output in the proper position to arrive simultaneously, ie when turning will travel different distances.
If they run in different directions, the distance run to the finish from a starting line will be somewhat higher in the case of giving more of a turn, and somewhat less for the other. As the entire track measures 500 meters, but do not know what it took to cross it first cycling, we can imagine it took some time t, so that its speed, assuming that remains constant, is 500 / t, while the other cyclist, who has remained at 5 meters from the finish, it will be 495 / t. If we place the starting line in a different position on the track, let's say x meters from the start, the slowest rider must go 500 - x m, while the fastest must travel 500 + x. As we arrive at the same time (500 + x) / (500 / t) = (500 - x) / (495 / t). In this equation it is clear that we can simplify the t, so that is (500 + x) / 500 = (500 - x) / 495, and removing denominators 495 * (500 + x) = 500 * (500 - x), where we 995x = 2500, so that x is 2500/995, approximately 2.5126 meters from the finish.
