Bunuel wrote:
Valve 1, if open, would fill a pool in 3 hours. Valve 2, if open, would fill the pool in 6 hours. If both valves are opened simultaneously, how long will it take to fill the pool to \(\frac{1}{5}\) of its capacity?
A. 18 minutes
B. 20 minutes
C. 24 minutes
D. 30 minutes
E. 36 minutes
Valve \(1\) can fill pool in \(3\) hours.
Valve \(1\) per hour rate of work \(= \frac{1}{3}\)
Valve \(2\) can fill pool in \(6\) hours.
Valve \(2\) per hour rate of work \(= \frac{1}{6}\)
\(1\) hour rate of work of Valve \(1\) and Valve \(2\) working together is;
\(\frac{1}{3} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6} = \frac{1}{2}\)
Both valves working together can fill the pool in \(= \frac{1}{(1/2)} = 2\) hours \(= 120\) minutes
Therefore both valves working together can fill the pool to \(\frac{1}{5}\) of its capacity in \(= \frac{1}{5} * 120 = 24\) minutes
Answer (C)...