Discussion
Pipe P can fill a tank in 38 hours. Pipe Q alone can fill it in 19 hours. Pipe R can empty the full tank in 133 hours. If all the pipes are opened together, how much time will be needed to make the tank full?
Answer: D
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).
\[ \frac{1}{38} + \frac{1}{19} - \frac{1}{133} \]
Over the common denominator 266:
\[ \frac{7 + 14 - 2}{266} = \frac{19}{266} = \frac{1}{14} \]
\[ t = 14 \text{ hours} \]
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