Three machines operating independently, simultaneously,

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Dec 05, 2017 9:36 am

Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48

The OA is B.

I made some calculus and I got 27. Experts, may you show me how to solve this PS question? Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Dec 05, 2017 9:36 am

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

by EconomistGMATTutor » Tue Dec 05, 2017 10:28 am

Hello Vincen.

Let's take a look at your question.

3 machines ------ 36 hours
4 machines ------- x hours

Then x=3*36/4 = 27 hours.

But the question says "in how many fewer hours..." Now, if 3 machines spend 36 hours and 4 machines spend 27 hours to do the work, then the work could be done in 9 hours less.

So, the correct answer is B.

I hope this explanation may help you.

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

Regards.

GMAT Prep From The Economist
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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Dec 05, 2017 10:45 am

Hi Vincen,

We're told that 3 machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. We're asked if one additional machine were used under the same operating conditions, in how many FEWER hours of simultaneous operation could the production order be fulfilled.

In these types of Work questions, it helps to determine how much work-time is needed to complete the job. Here, we have 3 machines working 36 hours each...

(3 machines)(36 hours each) = 108 machine-hours of work needed to complete the job.

Adding 1 additional machine creates the following equation:

(4 machines)(X hours each) = 108 machine-hours of work
X = 108/4 = 27 hours for each machine

The question asks for how many FEWER hours are needed... 36 hours - 27 hours = 9 fewer hours

Final Answer: B

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

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Oct 03, 2019 11:06 am

Vincen wrote:Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be fulfilled?

A. 6
B. 9
C. 12
D. 27
E. 48

The OA is B.

I made some calculus and I got 27. Experts, may you show me how to solve this PS question? Thanks.

If 3 machines working together take 36 hours to complete a job, then 1 machine by itself will take 3 times as long, or 3 x 36 = 108 hours to complete the same job. However, 4 machines working together will take Â¼ as long, or Â¼ x 108 = 27 hours to complete the job. Therefore, 1 additional machine (added to 3 machines) will save 36 - 27 = 9 hours.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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