A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills…
A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills $\dfrac{3}{8}$th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set Z are open, then how long will it take to fill 50% of the tank?
8 minutes
10 minutes
12 minutes
16 minutes
Solution
Set X (20 pipes): fills 0.7 tank in 14 min, rate = $0.05$ tank/min, per pipe = $0.0025$. Half of X (10 pipes) = $0.025$ tank/min. Set Y (10 pipes): fills $3/8$ in 6 min, rate = $0.0625$ tank/min, per pipe $= 0.00625$. Half of Y (5 pipes) = $0.03125$. Set Z (16 pipes): empties 0.5 tank in 20 min, rate = $-0.025$ tank/min. Net rate = $0.025 + 0.03125 - 0.025 = 0.03125$ tank/min. Time for 50% = $0.5/0.03125 = 16$ minutes.