Discussion
Two pipes P and Q can fill a tank in 10 hours and 14 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
Answer: B
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).
\[ \frac{1}{10} + \frac{1}{14} = \frac{7 + 5}{70} = \frac{6}{35} \]
\[ t = \frac{35}{6} = 5.8333 \text{ hours} \]
\[ 0.8333 \times 60 = 50 \text{ minutes} \]
So the tank fills in 5 hours 50 minutes.
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