An inlet pipe can fill a swimming pool in 9 hours and an outlet pipe can empty the pool in 12 hours. Through an error, both pipes are left open. How long will it take to fill te pool?

Answer:36 hours.Step-by-step explanation:Let x represent time taken by both pipes to fill the tank.We have been given that an inlet pipe can fill a swimming pool in 9 hours. So part of pool filled by inlet pipe in one hour would be [tex]\frac{1}{9}[/tex].We are also told that an outlet pipe can empty the pool in 12 hours. The part of pool emptied by outlet pipe in one hour would be [tex]\frac{1}{12}[/tex].Sine the time taken by both pipes to fill the tank is x hours, so part of pool filled by both pipes in one hour would be [tex]\frac{1}{x}[/tex].We will get an equation using our given information as:[tex]\frac{1}{x}=\frac{1}{9}-\frac{1}{12}[/tex]Let us solve for x.[tex]\frac{1}{x}=\frac{1*12}{9*12}-\frac{1*9}{12*9}[/tex][tex]\frac{1}{x}=\frac{12}{108}-\frac{9}{108}[/tex][tex]\frac{1}{x}=\frac{12-9}{108}[/tex][tex]\frac{1}{x}=\frac{3}{108}[/tex]Cross multiply:[tex]3x=108[/tex][tex]\frac{3x}{3}=\frac{108}{3}[/tex][tex]x=36[/tex]Therefore, it will take 36 hours for both pipes to fill the tank.