【Question 22】
A reservoir has five water pipes. To fill the reservoir, the first four pipes together need 6 hours; the last four pipes together need 8 hours. If only the first and fifth pipes are opened, it takes 12 hours to fill the reservoir. How many hours will it take to fill the reservoir if only the fifth pipe is used?
【Analysis and Solution】
Engineering problem.
Assume the entire pool is 1 unit;
$\left\{\begin{array}{r}\text { Pipe 1 }+ \text { Pipe 2 }+ \text { Pipe 3 }+ \text { Pipe 4 }=1 \div 6=\frac{1}{6} \\ \text { Pipe 2 }+ \text { Pipe 3 }+ \text { Pipe 4 }+ \text { Pipe 5 }=1 \div 8=\frac{1}{8} \\ \text { Pipe 1 }+ \text { Pipe 5 }=1 \div 12=\frac{1}{12}\end{array}\right.$
(2) + (3) - (1) $\div 2$, we get Pipe 5 $=\left(\frac{1}{8}+\frac{1}{12}-\frac{1}{6}\right) \div 2=\frac{1}{48}$;

If only Pipe 5 is used, it will take $1 \div \frac{1}{48}=48$ hours to fill the pool.