An inlet pipe can fill a water storage tank in 11 hours and an outlet pipe can empty the completely filled tank in 15 hours. If both pipes are opened simultaneously, what is the time taken to fill the empty tank (in hours)?

Question

Accepted Answer

Step 1: Calculate the rate of filling by the inlet pipe.
- Inlet pipe fills the tank in 11 hours, so rate = 1/11 tank per hour.

Step 2: Calculate the rate of emptying by the outlet pipe.
- Outlet pipe empties the tank in 15 hours, so rate = 1/15 tank per hour.

Step 3: Calculate the net rate when both pipes are open simultaneously.
- Net rate = (1/11) - (1/15) = (15 - 11) / (11 * 15) = 4 / 165 = 4/165 tank per hour.

Step 4: Calculate the total time to fill the tank at the net rate.
- Time = 1 / (4/165) = 165/4 = 41.25 hours.

Step 5: Convert 41.25 hours to mixed fraction.
- 41.25 = 41 + 0.25 = 41 + 1/4 = 41 1/4 hours.

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