Discussion
Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
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).
\[ \frac{1}{10} + \frac{1}{15} - \frac{1}{w} = \frac{1}{18} \]
\[ \frac{3 + 2}{30} - \frac{1}{w} = \frac{1}{18} \quad\Longrightarrow\quad \frac{1}{6} - \frac{1}{w} = \frac{1}{18} \]
\[ \frac{1}{w} = \frac{3 - 1}{18} = \frac{1}{9} \quad\Longrightarrow\quad w = 9 \text{ minutes} \]
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