2008 Gauss 8 Problem 25

Chantelle had two candles, one of which was 32 cm longer than the other. She lit the longer one at 3 p.m. and lit the shorter one at 7 p.m. At 9 p.m., they were both the same length. The longer one was completely burned out at 10 p.m. and the shorter one was completely burned at midnight. The two candles burned at different, but constant, rates. What was the sum of the original lengths of the two candles?

\textbf{(A)}\ 42 \text{ cm}\quad \textbf{(B)}\ 48 \text{ cm}\quad \textbf{(C)}\ 60 \text{ cm}\quad \textbf{(D)}\ 80 \text{ cm}\quad \textbf{(E)}\ 52 \text{ cm}

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 Gauss contests here.