2002 Pascal Problem 15

In the diagram, ABC represents a triangular jogging path. Jack jogs along the path from A to B to F. Jill jogs from A to C to F. Each jogs the same distance. The distance from F to B, in metres, is

\textbf{(A)}\ 40\quad \textbf{(B)}\ 120\quad \textbf{(C)}\ 100\quad \textbf{(D)}\ 80\quad \textbf{(E)}\ 200

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 Pascal contests here.