Discussion
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Answer: C
Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).
\[ \frac{1}{5} + \frac{1}{6} - \frac{1}{12} \]
Over the common denominator 60:
\[ \frac{12 + 10 - 5}{60} = \frac{17}{60} \text{ per hour} \]
\[ t = \frac{60}{17} = 3\tfrac{9}{17} \text{ hours} \]
The emptying pipe subtracts, so the tank still fills - but more slowly than the \( 2\tfrac{8}{11} \) hours A and B would manage alone.
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