AMC 12 Mock Exam 3 Problem 3

Problem 3 of 25

An empty tank can be filled by pipe $A$ alone in $6$ hours or by pipe $B$ alone in $9$ hours, and a drain at the bottom of the tank can empty a full tank in $18$ hours. A worker opens both pipes and, by mistake, also leaves the drain open, all starting at the same moment. How many hours does it take to fill the empty tank?

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Solution

Per hour, pipe $A$ fills $\frac16$ of the tank, pipe $B$ fills $\frac19$ , and the drain removes $\frac1{18}$ . The net rate is $\frac{3+2-1}{18}=\frac29$ tank per hour, so the tank fills in $\boxed{\tfrac92}$ hours.

Tagged: combined work rates

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