Problem Solving

AAPL wrote:GMAT Prep

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

OA B

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

Two of the large hoses would fill the pool in 10 minutes. Two of the small hoses would fill the pool in 15 minutes. We have one large and one small hose, so the time must be in between 10 and 15 minutes, and among the answers, only 12 minutes makes sense.

AAPL wrote:GMAT Prep

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

OA B

We are given that the large hose takes 20 minutes to fill a swimming pool and that the small hose takes 30 minutes to fill the same swimming pool.

Since rate = work/time, the rate of the large hose is 1/20, and the rate of the small hose is 1/30.

We need to determine the number of minutes, when working simultaneously, it will take both hoses to fill the swimming pool. To solve, we can use the combined worker formula.

work of the large hose + work of the small hose = total work

Since the pool is being filled, the total work completed is 1 job. We can also let the time worked, in minutes, for both hoses, equal the variable t. Using the formula work = rate x time, we express the work of each hose as follows:

work of the large hose = (1/20)t

work of the small hose = (1/30)t

Lastly, we can determine t:

work of the small hose + work of the large hose = 1

(1/20)t + (1/30)t = 1

(3/60)t + (2/60)t = 1

(5/60)t = 1

t = 1/(5/60)

t = 60/5

t = 12

Alternate Solution:

In one minute, the larger hose can fill 1/20 of the pool, and the smaller hose can fill 1/30 of the pool. If they are used simultaneously, they fill 1/20 + 1/30 = 5/60 = 1/12 of the pool in one minute. If they fill 1/12 of the pool in one minute, they will fill 12/12 of the pool in 12 minutes.

Answer: B