Problem Solving

BTGmoderatorDC wrote:The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?

(A) 0.22
(B) 0.31
(C) 2.50
(D) 3.21
(E) 4.56

OA D

Source: Official Guide

Given that the first outlet, flowing at a constant rate, can fill a swimming pool in 9 hours, the part of the pool filled in 1 hour = 1/9; and the second outlet, flowing at a constant rate, can fill a swimming pool in 5 hours, the part of the pool filled in 1 hour = 1/5

Part of the pool filled in 1 hour if both the outlets are open = 1/9 + 1/5 = 14/45

Thus, the hours needed to fill the pool = 45/14 = 3.21 hours

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC wrote:The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?

(A) 0.22
(B) 0.31
(C) 2.50
(D) 3.21
(E) 4.56

OA D

Source: Official Guide

One approach is to assign a NICE NUMBER to the volume of the swimming pool. This number will work well with the two pieces of information (fill pool in 9 hours and fill pool in 5 hours).
So, let's say that the volume of the pool is 45 gallons.

The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours
So, this outlet pumps at a rate of 5 gallons per hour

The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours.
So, this outlet pumps at a rate of 9 gallons per hour

If both outlets are used at the same time. . .
The combined rate of both pumps = (5 gallons per hour) + (9 gallons per hour)
= 14 gallons per hour

Time = output/rate
At 14 gallons per hour, the time to pump 45 gallons = 45/14
= 3 3/14
= 3.something

Answer: D

Cheers,
Brent

Hi All,

This question is a standard "Work Formula" question. When you have 2 entities sharing a task, you can use the following formula to figure out how long it takes for the 2 entities to complete the task together.

Work = (A)(B)/(A+B) where A and B are the individual times required to complete the task

Here, we're given the rates as 9 hours and 5 hours. Using the Work Formula, we have...

(9)(5)/(9+5) = 45/14

45/14 is a little more than 3.....there's only one answer that matches...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote:The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?

(A) 0.22
(B) 0.31
(C) 2.50
(D) 3.21
(E) 4.56

The combined rate of the first and second outlets is:

1/9 + 1/5 = 5/45 + 9/45 = 14/45

Thus, the combined fill rate is 14/45 of the pool in one hour. So the time it would take both outlets to fill the pool is 45/14 ≈3.21 hours.

Answer: D

BTGmoderatorDC wrote:The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?

(A) 0.22
(B) 0.31
(C) 2.50
(D) 3.21
(E) 4.56

The combined rate of the first and second outlets is:

1/9 + 1/5 = 5/45 + 9/45 = 14/45

Thus, the combined fill rate is 14/45 of the pool in one hour. So the time it would take both outlets to fill the pool is 45/14 ≈3.21 hours.

Answer: D