A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank...

[AAPL]

GMAT Prep

A small pump water would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?

A. 1/4
B. 1/3
C. 2/5
D. 5/4
E. 3/2

OA C

[Scott@TargetTestPrep]

GMAT Prep

A small pump water would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?

A. 1/4
B. 1/3
C. 2/5
D. 5/4
E. 3/2

OA C

Solution:

Recall that rate = work/time. Therefore, the rate of the first pump is 1/2. The rate of the larger pump is 1 / (1/2) = 2.

The combined rate of the two pumps is 1/2 + 1/(1/2) = 1/2 + 2 = 5/2. Since time is the inverse of rate, it will take them 1/(5/2) = 2/5 of an hour to fill the empty tank working simultaneously.

Answer: C