2016 Cayley Problem 22

Alain and Louise are driving on a circular track with radius 25 km. Alain leaves the starting line first, going clockwise around the track at a speed of 80 km/h. Fifteen minutes after Alain starts, Louise leaves the same starting line, going counterclockwise around the track at a speed of 100 km/h. For how many hours will Louise have been driving when the two of them pass each other for the fourth time?

\textbf{(A)}\ \frac{50\pi-6}{45}\quad \textbf{(B)}\ \frac{4\pi+1}{4}\quad \textbf{(C)}\ \frac{10\pi-1}{9}\quad \textbf{(D)}\ \frac{15\pi+6}{16}\quad \textbf{(E)}\ \frac{25\pi-1}{24}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.