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 counter- clockwise 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?
Answer Choices
A. \frac{50\pi-6}{45}
B. \frac{4\pi+1}{4}
C. \frac{10\pi-1}{9}
D. \frac{15\pi+6}{16}
E. \frac{25\pi-1}{24}