Discussion
Tap P alone fills a cistern in 2 hours; while tap Q alone fills the same cistern in 3 hours. A new tap R is attached to the bottom of the cistern which can empty the completely filled cistern in 6 hours. Sunny started all three taps together at 9am. When will the tank be full?
Answer: A
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).
\[ \frac{1}{2} + \frac{1}{3} - \frac{1}{6} = \frac{3 + 2 - 1}{6} = \frac{2}{3} \text{ per hour} \]
\[ t = \frac{1}{2/3} = 1.5 \text{ hours} \]
\[ 9{:}00 + 1{:}30 = \textbf{10{:}30 a.m.} \]
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