1967 AHSME Problem 27

Two candles of the same length are made of different materials so that one burns out completely at a uniform rate in 3 hours and the other in 4 hours. At what time P.M. should the candles be lighted so that, at 4 P.M., one stub is twice the length of the other?

\textbf{(A)}\ 1:24\qquad \textbf{(B)}\ 1:28\qquad \textbf{(C)}\ 1:36\qquad \textbf{(D)}\ 1:40\qquad \textbf{(E)}\ 1:48

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.