2001 Fermat Problem 19

Cindy leaves school at the same time every day. If she cycles at 20 km/h, she arrives home at 4:30 in the afternoon. If she cycles at 10 km/h, she arrives home at 5:15 in the afternoon. At what speed, in km/h, must she cycle to arrive home at 5:00 in the afternoon?

\textbf{(A)}\ 16\frac{2}{3}\quad \textbf{(B)}\ 15\quad \textbf{(C)}\ 13\frac{1}{3}\quad \textbf{(D)}\ 12\quad \textbf{(E)}\ 18\frac{3}{4}

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 Fermat contests here.