Working alone, pump A can empty a pool in 3 hours...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Working alone, pump A can empty a pool in 3 hours...

by BTGmoderatorLU » Fri Jan 12, 2018 2:15 pm

Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how how many minutes will it take pump A and pump B to empty the pool?

(A) 72
(B) 75
(C) 84
(D) 96
(E) 108

The OA is A.

I'm confused with this PS question. Experts, any suggestion? I don't know how can I solve it. Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Fri Jan 12, 2018 2:15 pm

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sat Jan 13, 2018 8:51 am

Hello LUANDATO.

Let's take a look at your question.

Working alone, pump A can empty a pool in 3 hours, it implies that pump A wor at a rate 1/3 pool/hour.
Working alone, pump B can empty a pool in 2 hours, it implies that pump A wor at a rate 1/2 pool/hour.

Working together the rate will be equal to $$\frac{1}{3}+\frac{1}{2}=\frac{5}{6}\ \text{pool per hour}$$. Now we have the following: $$\frac{5\ }{6\ }\ \frac{pool}{60\ \min}=1\ \frac{pool}{x}\ \Leftrightarrow\ x=72\ \min.$$ This is why the correct answer is the option [spoiler]A=72[/spoiler].

I hope this answer may help you.

I'm available if you'd like a follow-up.

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Aug 11, 2019 6:50 pm

BTGmoderatorLU wrote:Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how how many minutes will it take pump A and pump B to empty the pool?

(A) 72
(B) 75
(C) 84
(D) 96
(E) 108

The combined rate of pumps A and B is:

1/3 + 1/2 = 2/6 + 3/6 = 5/6, so the time is 1/(5/6) = 6/5 hours, which is 6/5 x 60 = 72 minutes.

Answer: A

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