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Two pipes A and B can fill a tank in 20 and 30 hours, respectively. Both pipes are opened to fill the tank, but when the tank is one-third full, a leak develops through which one-fourth of the water supplied by both pipes goes out. Find the total time (in hours) taken to fill the tank.

1. 14⅔
2. 14
3. 11⅖
4. 12⅓

Correct answer: 14⅔

Solution

Pipe A fills in 20 h and B in 30 h, so together they fill at $\frac{1}{20}+\frac{1}{30}=\frac{1}{12}$ tank per hour. One-third of the tank is filled in 4 hours; after that, only $\frac{3}{4}$ of the combined supply is effective, so the net rate becomes $\frac{3}{4}\times\frac{1}{12}=\frac{1}{16}$ tank per hour. The remaining two-thirds takes $\frac{2/3}{1/16}=10\frac{2}{3}$ hours, giving total time $4+10\frac{2}{3}=14\frac{2}{3}$ hours.

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