smc

Let the rate of water flowing through valve $A$ be $a$, the rate of water flowing through valve $B$ be $b$, and the rate of water flowing through valve $C$ be $c$. WLOG, let the volume of the tank be 1 liter, and let the units for the rates be liters per hour. With this information, we can write three equations. $$\frac{1}{a+b+c}=1$$ $$\frac{1}{a+c}=\frac{3}{2}$$ $$\frac{1}{b+c}=2$$ Manipulate each equation to get $$1=a+b+c$$ $$\frac{2}{3}=a+c$$ $$\frac{1}{2}=b+c$$ Solving for $a$ yields $a=\frac{1}{2}$, and solving for $b$ yields $b=\frac{1}{3}$. The number of hours to fill the tub with only valves $A$ and $B$ on is $\frac{1}{\frac{1}{2}+\frac{1}{3}}=\frac{6}{5}=\boxed{1.2}$.