Answer:
40 hours will it take for the pool to fill.
Step-by-step explanation:
A pump can fill a swimming pool in 8 hours.
Work done by pump to fill in 1 hour is [tex]\frac{1}{8}[/tex]
The pool also has a drain that can empty the pool in 10 hours.
Work done by pump to drain in 1 hour is [tex]\frac{1}{10}[/tex]
If someone turns on the pump to fill the pool, but forgets to shut the drain.
Work done by both pipe in 1 hour is
[tex]W=\frac{1}{8}-\frac{1}{10}[/tex]
[tex]W=\frac{10-8}{80}[/tex]
[tex]W=\frac{2}{80}[/tex]
[tex]W=\frac{1}{40}[/tex]
Both pipe filled [tex]\frac{1}{40}[/tex] part of pool in hours = 1
Both pipe filled complete pool in hours = [tex]\frac{1}{\frac{1}{40}}=40[/tex]
Therefore, 40 hours will it take for the pool to fill.
