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Register now and save up to $200 Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code ## Machine A and B This topic has 4 expert replies and 1 member reply ### Top Member lheiannie07 Master | Next Rank: 500 Posts Joined 07 Sep 2017 Posted: 203 messages Followed by: 1 members #### Machine A and B Wed Sep 13, 2017 3:41 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job? A. 12hrs B. 16hrs C. 24hrs D. 28hrs E. 32hrs Is there a strategic approach to this? Experts help please. Thanks OA C Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13500 messages Followed by: 1791 members Thanked: 12992 times GMAT Score: 790 Wed Sep 13, 2017 4:01 am lheiannie07 wrote: Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job? A. 12hrs B. 16hrs C. 24hrs D. 28hrs E. 32hrs Let the job = 72 widgets. Since A takes 24 hours to complete the job, A's rate = w/t = 72/24 = 3 widgets per hour. At a rate of 3 widgets per hour, the work produced by A in 8 hours = rt = 3*8 = 24 widgets. Remaining work = 72-24 = 48 widgets. Since B's rate is 2/3 of A's rate, B's rate = (2/3)(3) = 2 widgets per hour. At a rate of 2 widgets per hour, the time for B to produce the remaining 48 widgets = w/r = 48/2 = 24 hours. The correct answer is C. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "Thank" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Thanked by: lheiannie07 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2380 messages Followed by: 115 members Thanked: 1121 times GMAT Score: 770 Wed Sep 13, 2017 6:07 am lheiannie07 wrote: Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job? A. 12hrs B. 16hrs C. 24hrs D. 28hrs E. 32hrs Is there a strategic approach to this? Experts help please. Thanks OA C If machine A can complete the job in 24 hours, and it works for 8 hours, then it has completed 8/24 or 1/3 of the job, leaving 2/3 of the job for B to complete. If Machine A's rate was 1 job/24 hours, or 1/24, and B's rate is 2/3 of this, then B's rate is (2/3) * (1/24) = 1/36. If Machine B works for T hours at a rate of 1/36 and must complete 2/3 of a job, we get the following equation: (1/36) * T = 2/3 --> T = 24; The answer is C _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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DavidG@VeritasPrep Legendary Member
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Wed Sep 13, 2017 6:10 am
lheiannie07 wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

Is there a strategic approach to this? Experts help please. Thanks

OA C
Another approach. If Machine A has worked for 8 hours, and it takes Machine A 24 hours to complete the job, it would take Machine A an additional 16 hours to finish the job alone.

Rate and Time have a reciprocal relationship. If B's rate is 2/3 of A's rate, then it would take B 3/2 of A's Time to complete the job. If it would have taken A 16 hours to complete the job, it would take B 16*(3/2) or 24 hours. The answer is C.

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Wed Sep 20, 2017 2:39 pm
lheiannie07 wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs
The rate of Machine A is 1/24, so in 8 hours, 1/3 of the job is completed, and thus 2/3 of the job is left to be completed.

If the rate of Machine B is 2/3 that of Machine A, then the rate of Machine B is (2/3)(1/24) = 1/36.

Thus, it will take Machine B (2/3)/(1/36) = 2/3 x 36 = 24 hours to complete the rest of the job.

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### Top Member

lheiannie07 Master | Next Rank: 500 Posts
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Fri Sep 22, 2017 1:07 pm
Thank you so much for the solution, but is there an easier way to solve this?

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