Three race tracks made from semi-circles

All three runners finish at the same time.

Let the radius of R's track be r and let the radius of the first semicircle of P's track be p; then the radius of the second circle of this track is r-p.

The total length of P's track is pp + p(r-p) = pr, the same length as R's track.

By a similar argument, the length of Q's track is also pr.