At a constant Rate of flow, it takes \(20\) minutes to fill a swimming pool if a large hose is used and \(30\) minutes

[M7MBA]

At a constant Rate of flow, it takes \(20\) minutes to fill a swimming pool if a large hose is used and \(30\) minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?

A. 10
B. 12
C. 15
D. 25
E. 50

Answer: B

Source: GMAT Prep

[Brent@GMATPrepNow]

At a constant Rate of flow, it takes \(20\) minutes to fill a swimming pool if a large hose is used and \(30\) minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?

A. 10
B. 12
C. 15
D. 25
E. 50

Answer: B

Source: GMAT Prep

Let's assign a nice value to the volume of the pool. We want a volume that works well with the given information (20 minutes and 30 minutes).
So, let's say the pool has a total volume of 60 gallons

It takes 20 minutes to fill a swimming pool with a LARGE hose
In other words, the LARGE hose can pump 60 gallons of water in 20 minutes
So, the RATE of the large hose = 3 gallons per minute

It takes 30 minutes to fill a swimming pool with a SMALL hose
In other words, the SMALL hose can pump 60 gallons of water in 30 minutes
So, the RATE of the small hose = 2 gallons per minute

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

How many minutes will it take to fill the pool when both hoses are used simultaneously?
We need to pump 60 gallons of water, and the combined rate is 5 gallons per minute
Time = output/rate
= 60/5
= 12 minutes

Answer: B

Cheers.
Brent