Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and

VJesus12 wrote: ↑

Tue May 04, 2021 6:26 am

Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?

A. 3.25
B. 3.6
C. 4.2
D. 4.4
E. 5.5

Answer: B

Source: GMAT Paper Tests

Let's assign a nice value to the volume of the tank. We want a volume that works well with the given information (1/2, 2/3, 3 hours and 6 hours).
So, let's say the tank has a total volume of 18 gallons

One inlet pipe fills an empty tank to 1/2 of capacity in 3 hours
1/2 the tank is 9 gallons.
So, this pipe fills 9 gallons in 3 hours.
So, the RATE of this pipe = 3 gallons per hour

A second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours
2/3 the tank is 12 gallons.
So, this pipe fills 12 gallons in 6 hours.
So, the RATE of this pipe = 2 gallons per hour

So, the COMBINED rate of BOTH pumps = 3 gallons per hour + 2 gallons per hour = 5 gallons per hour

How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
We need to pump 18 gallons of water, and the combined rate is 5 gallons per hour
Time = output/rate
= 18/5
= 3.6 hours

Answer: B

Cheers.
Brent