Question

the intake pipe can fill a certain tank in 6 hours when the outlet pipe is closed, but with the outlet pipe open it takes 9 hours. How long would it take the outlet pipe to empty a full tank?

Answer 1

The outlet pipe will take 18 hours to empty the tank.

Step-by-step explanation:

Number of hours taken by inlet pipe to fill the tank=6

work done by the inlet pipe in 1 hour=1/6

Number of hours taken by the inlet pipe to fill the tank with the outlet pipe open=9

work done by the inlet pipe in 1 hour with outlet  pipe open=1/9

we have to determine the time taken by the outlet pipe to empty the tank

The inlet and outlet pipe does the opposite work.

$\\time\ taken\ by\ the\ outlet\ pipe\ to\ empty\ the\ tank=x\\work\ done\ by\ the\ outlet\ pipe\ in\ 1\ hour=1/x\\(1/6-1/x)9=1\\1/6-1/x=1/9\\1/x=1/6-1/9=3/54\\x=54/3=18$

The outlet pipe takes 18 hours to empty the tank.