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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Three machines, A, B, and C, can complete a certain tagged by: M7MBA ##### This topic has 3 expert replies and 0 member replies ## Three machines, A, B, and C, can complete a certain Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job? A. 4/5 B. 9/4 C. 11/4 D. 4 E. 13/2 The OA is the option B. Experts, may you help me here? I am confused. What formulas should I set here? ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14945 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 Top Reply M7MBA wrote: Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job? A. 4/5 B. 9/4 C. 11/4 D. 4 E. 13/2 Let the task = the LCM of 10, 4 and 5 = 20 units. Since A takes 10 hours to complete the 20-unit task, A's rate = w/t = 20/10 = 2 units per hour. Since B takes 4 hours to complete the 20-unit task, B's rate = w/t = 20/4 = 5 units per hour. Since C takes 5 hours to complete the 20-unit task, C's rate = w/t = 20/5 = 4 units per hour. In 1 hour, the work produced by A+B+C = 2+5+4 = 11 units. Remaining work = 20-11 = 9 units. Since C's rate = 4 units per hour, the time for C to produce the remaining 9 units = w/r = 9/4 hours. The correct answer is B. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 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 Elite Legendary Member Joined 23 Jun 2013 Posted: 9955 messages Followed by: 493 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi M7MBA, We're told that three Machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively and that all 3 machines worked together for 1 hour and then STOP. We're asked for the number of hours it would then take Machine C to complete the job on its own. Since we have 3 entities working on a task together, we can convert their work rates into 'fraction of the job completed per hour'... Machine A = 10 hours to complete a job alone = 1/10 of the job completed per hour. Machine B = 4 hours to complete a job alone = 1/4 of the job completed per hour. Machine C = 5 hours to complete a job alone = 1/5 of the job completed per hour. Thus, after 1 hour is done, a total of 1/10 + 1/4 + 1/5 = 2/20 + 5/20 + 4/20 = 11/20 of the job is done This means that 1 - 11/20 = 9/20 of the job still has to be completed. Machine C completes 4/20 of the job each hour, so it would take (9/20) / (4/20) = 9/4 hours for Machine C to complete the job. Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1781 messages Followed by: 14 members Upvotes: 43 M7MBA wrote: Three machines, A, B, and C, can complete a certain task in 10 hours, 4 hours, and 5 hours respectively. If all 3 machines worked together for 1 hour and then stop, how many hours does it take machine C to complete the job? A. 4/5 B. 9/4 C. 11/4 D. 4 E. 13/2 The combined rate of A, B, and C is: 1/10 + 1/4 + 1/5 = 2/20 + 5/20 + 4/20 = 11/20. So if all the machines work for 1 hour, 11/20 of the job is completed, and 9/20 is left to be completed. Thus, it would take machine C (9/20)/(1/5) = 45/20 = 9/4 hours to complete the job. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO • FREE GMAT Exam Know how you'd score today for$0

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