AHSME 1973 Problem 14

Each valve $A$, $B$, and $C$, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves $A$ and $C$ open it takes 1.5 hours, and with only valves $B$ and $C$ open it takes 2 hours. The number of hours required with only valves $A$ and $B$ open is $\textbf{(A)}\ 1.1 \textbf{(B)}\ 1.15 \textbf{(C)}\ 1.2 \textbf{(D)}\ 1.25 \textbf{(E)}\ 1.75$