9. (10 points) A water pool has three inlets and one outlet. When the outlet and any two of the inlets are opened simultaneously, it takes 6 hours, 5 hours, and 4 hours respectively to fill the entire pool; when the outlet and all three inlets are opened simultaneously, it takes 3 hours to fill the entire pool. If all three inlets are opened simultaneously without opening the outlet, how many hours will it take to fill the entire pool? $\qquad$
【Analysis】This problem requires the method of finding differences among similarities. The three times are 6 hours, 5 hours, and 4 hours, all compared with 3 hours. For example, $\frac{1}{3}-\frac{1}{6}=\frac{1}{6}$ is the efficiency of one of the inlet pipes. To make it more intuitive for students, I will use the method of setting letters.

【Solution】Solution: Let the three inlet pipes fill the entire water tank alone in $a$, $b$, and $c$ hours, respectively, and the outlet pipe drains the entire water tank in $x$ hours,
(1) $\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}-\frac{1}{\mathrm{x}}=\frac{1}{6}$,
(2) $\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{c}}-\frac{1}{\mathrm{x}}=\frac{1}{5}$,
(3) $\frac{1}{b}+\frac{1}{c}-\frac{1}{x}=\frac{1}{4}$,
(4) $\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{~b}}+\frac{1}{\mathrm{c}}-\frac{1}{\mathrm{x}}=\frac{1}{3}$,

Solving: (4) - (3) $\frac{1}{\mathrm{a}}=\frac{1}{12}$
(4) - (2) $\frac{1}{b}=\frac{2}{15}$,
(4) - (1) $\frac{1}{\mathrm{c}}=\frac{1}{6}$,
$1 \div\left(\frac{1}{12}+\frac{2}{15}+\frac{1}{6}\right)=2 \frac{14}{23}$.
Therefore, the answer is: $2 \frac{14}{23}$.