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Pipes P and Q can completely fill a water tank in 10 hours and 15 hours, respectively. A pipe R can empty a tank filled completely with water in 12 hours. Initially, the tank is empty and only pipes P and Q are opened at 6 a.m., and pipe R is also opened at 9 a.m. By what time will the tank be completely filled?

1. 1 p.m.
2. 2 p.m.
3. 11 a.m.
4. 3 p.m.

Correct answer: 3 p.m.

Solution

P fills 1/10 tank per hour and Q fills 1/15 tank per hour, so together they fill 1/6 tank per hour. From 6 a.m. to 9 a.m., they fill 3 × 1/6 = 1/2 tank. After 9 a.m., R empties 1/12 tank per hour, so net rate = 1/10 + 1/15 - 1/12 = 1/12 tank per hour. The remaining half tank takes 6 hours, so the tank is full at 3 p.m.

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