[tex]18h[/tex]
1) According to the text, since we have a pipe to fill it in and a drain to empty the pool and we were told to find how long will it take to fill the pool we can write out the following rational equation:
[tex]\begin{gathered} \frac{t}{15}-\frac{t}{40}=1-\frac{1}{4} \\ \frac{t}{15}-\frac{t}{40}=\frac{3}{4} \\ \frac{120\div15\times t}{120}-\frac{120\div40\times t}{120}=\frac{30\times3}{120} \\ \frac{8t}{120}-\frac{3t}{120}=\frac{90}{120}\times120 \\ 8t-3t=90 \\ 5t=90 \\ \frac{5t}{5}=\frac{90}{5} \\ t=18 \end{gathered}[/tex]
Note that since there is already 1/4 of the capacity of that pool, the sum of the filling pipe minus the draining pipe is going to be equal to 1 (full pool) - 1/4=3/4
2) So, the answer is:
[tex]18h[/tex]
