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The water from one outlet, flowing at a constant rate, can

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The water from one outlet, flowing at a constant rate, can

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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

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GMAT/MBA Expert

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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
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

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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

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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
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

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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For pipe 1 = Work done in 1 hour = 1/9 (rate)
For pipe 2 = Work done in 1 hour = 1/5 (rate)

Work done = Rate x Time
$$1=\left(\frac{1}{9}+\frac{1}{5}\right)\cdot x$$
$$1=\frac{\left(5+9\right)}{45}\cdot x$$
$$1=\frac{14}{45}\cdot x$$
$$45=14\cdot x$$
$$x=\frac{45}{14}=3.21$$

Option D is correct.....

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