A water tank has an inlet pipe and a drain pipe A full tank

A water tank has an inlet pipe and a drain pipe.
A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?

Solution

Drain DATA:
time = 1/2 hr/job ; rate = 2 jobs/hour
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Inlet pipe DATA:
time = 3/4 hr/job ; rate = 4/3 job/hr.
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Together DATA:
time = x hrs/job ; rate = 1/x job/hr.
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Equation:
Inlet pipe rate - Drain pipe rate = together rate
4/3 - 1/2 = 1/x
Multiply thru by 6x to get:
8x - 3x = 6
5x = 6
x = 6/5 hours = 1 hr 12 minutes (time to empty the tank)