3.45 When valves $A, B, C$ are each opened, water flows into the tank at a constant rate. When all three valves are open, it takes 1 hour to fill the tank; when only valves $A, C$ are open, it takes 1.5 hours; if only valves $B, C$ are open, it takes 2 hours. Then, when only valves $A, B$ are open, the number of hours required to fill the tank is
(A) 1.1 .
(B) 1.15 .
(C) 1.2 .
(D) 1.25 .
(E) 1.75 .
(24th American High School Mathematics Examination, 1973)
[Solution] Let $x, y, z$ be the amounts of water (in terms of the tank's capacity) that valves $A, B, C$ respectively fill into the tank in one hour. Then we have
$$
\left\{\begin{array}{l}
x+y+z=1, \\
x+z=\frac{1}{1.5}, \\
y+z=\frac{1}{2} .
\end{array}\right.
$$
(1) $\times$ (2) - (2) - (3) gives $x+y=\frac{5}{6}$, which means $\frac{6}{5}(x+y)=1$. Therefore, opening valves $A$ and $B$ to fill the tank will take $\frac{6}{5}=1.2$ hours. Hence, the answer is $(C)$.