if the inlet pipe for a tank is opened, the tank will be filled in 6 hours. If the outlet pipe for a tank is opened when the tank is full, the tank will be emptied in 8 hours. How long will it take to completely fill the empty tank if both the inlet and outlet pipes are open

Answer:24 hoursStep-by-step explanation:We know that a tank can be filled completely by an inlet pipe in 6 hours and the same full tank can be emptied in 8 hours when the outlet pipe is open.We are to find the time it takes to completely fill the empty tank if both the inlet and outlet pipes are open.Assuming the time taken to fill the tank when both the pipes are open together be x, we can write an equation:[tex]\frac{1}{x} =\frac{1}{6} -\frac{1}{8}[/tex]Solving for x:[tex]\frac{1}{x} =\frac{4-3}{24} =\frac{1}{24}[/tex][tex]x=24[/tex]Therefore, it will take 24 hours to completely fill the tank with both pipes open.