36mba
One water pump can fill half of a certain empty tank in 3 hours. Another pump can fill half of the same tank in \(3\frac{1}{2}\) hours. Working together, how long will it take these two pumps to fill the entire tank?
(A) \(1\frac{7}{13}\)
(B) \(1\frac{5}{8}\)
(C) \(3\frac{1}{4}\)
(D) \(3\frac{3}{13}\)
(E) \(3\frac{1}{2}\)
We are given that a water pump can fill half of a certain tank in 3 hours; thus, the rate of the pump is (1/2)/3 = 1/6. We are given that another pump can fill 1/2 of the same tank in 3½, or 7/2, hours. Thus, the rate of the second pump is (1/2)/(7/2) = 2/14 = 1/7. If we let t = the time it takes the two pumps working together to fill the entire tank, and if we let 1 equal the work (i.e., filling the entire tank) needed to be completed, we can create the following equation and determine t:
(1/6)t + (1/7)t = 1
Multiplying the entire equation by 42, we have:
7t + 6t = 42
13t = 42
t = 42/13 = 3 3/13
Answer: D