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Let the rate that hose $A$ fills the pool be equal to $A$, and similarly for hoses $B$ and $C$. Then, let $P$ be equal to the volume of the pool. From the given information, we can write the equation $P=4(A+B)$, which just says the pool volume is equal to the rate it is being filled, multiplied by the time taken to fill it. We can rewrite this as $\frac{P}{4}=A+B$. Doing this with the rest of the given information, we can write three equations: $$\frac{P}{4}=A+B$$ $$\frac{P}{5}=A+C$$ $$\frac{P}{6}=B+C$$ Adding these three equations, we can simplify as shown: $$\begin{array}{rl}\frac{P}{4}+\frac{P}{5}+\frac{P}{6}& =(A+B)+(A+C)+(B+C)\\ \Rightarrow \frac{15P}{60}+\frac{12P}{60}+\frac{10P}{60}& =2(A+B+C)\\ \Rightarrow 37P& =120(A+B+C)\\ \Rightarrow P& =\frac{120}{37}(A+B+C)\end{array}$$ Looking carefully at the final expression here, we can see that $A+B+C$ is the rate that the pool would be filled with all three hoses working together. So, $\frac{120}{37}\approx \boxed{3.24}$ is equal to the number of hours it would take all three hoses to fill the pool.