Discussion
Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate of 34 litres per minute. P, Q and R operate at a constant rate.
If it takes one hour to completely empty a full storage tank with all the pipes operating simultaneously, what is the capacity of the storage tank (in litres)?
Answer: C
The tank holds 120 litres.
Let the capacity be \(C\) litres. P fills at \(C/10\) litres per minute and Q at \(C/6\), while R removes 34 litres per minute. With all three running, the full tank empties in 60 minutes, so the net outflow is \(C/60\) litres per minute:
\[ \begin{aligned} 34 - \frac{C}{10} - \frac{C}{6} &= \frac{C}{60} \\ 34 &= \frac{6C + 10C + C}{60} = \frac{17C}{60} \\ C &= 120 \end{aligned} \]
Check: P adds 12, Q adds 20 and R removes 34 litres per minute, a net loss of 2 litres per minute, which empties 120 litres in exactly 60 minutes. With 60 litres, P and Q would add only 16 litres per minute against R’s 34, emptying the tank in under 4 minutes rather than an hour; 26.8 and 127.5 do not satisfy the equation either.
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