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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 At Supersonic Corporation, the time required for a machine.. tagged by: BTGmoderatorLU This topic has 1 expert reply and 0 member replies Top Member At Supersonic Corporation, the time required for a machine.. At Supersonic Corporation, the time required for a machine to complete a job is determined by the formula: $$t=\sqrt{w}+\sqrt{\left(w-1\right)}$$ where w = the weight of the machine in pounds and t = the hours required to complete the job. If machine A weighs 8 pounds, and machine B weighs 7 pounds, how many hours will it take the two machines to finish one job if they work together? $$A.\ \frac{6}{7-\sqrt{3}}$$ $$B.\ \frac{1}{2}\left(\sqrt{8}+\sqrt{6}\right)$$ $$C.\ \frac{1}{3}\left(6-\sqrt{3}\right)$$ $$D.\ 3\left(\sqrt{3}+\sqrt{2}\right)$$ $$E.\ \sqrt{8}+2\sqrt{7}+\sqrt{6}$$ The OA is B. In this case, I just need to do the following, Can I say that the total time will be, Time of machine A + time of machine B, right? Then, $$T_A=\sqrt{8}+\sqrt{8-1}=\sqrt{8}+\sqrt{7}$$ And $$T_B=\sqrt{7}+\sqrt{7-1}=\sqrt{7}+\sqrt{6}$$ Finally, $$T_{total}=\left(\sqrt{8}+\sqrt{7}\right)+\left(\sqrt{7}+\sqrt{6}\right)=\sqrt{8}+2\sqrt{7}+\sqrt{6}$$ But, how can I get the combined time? I'm really confused by this PS question. Experts, any suggestion? Thanks in advance. GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: At Supersonic Corporation, the time required for a machine to complete a job is determined by the formula: $$t=\sqrt{w}+\sqrt{\left(w-1\right)}$$ where w = the weight of the machine in pounds and t = the hours required to complete the job. If machine A weighs 8 pounds, and machine B weighs 7 pounds, how many hours will it take the two machines to finish one job if they work together? $$A.\ \frac{6}{7-\sqrt{3}}$$ $$B.\ \frac{1}{2}\left(\sqrt{8}+\sqrt{6}\right)$$ $$C.\ \frac{1}{3}\left(6-\sqrt{3}\right)$$ $$D.\ 3\left(\sqrt{3}+\sqrt{2}\right)$$ $$E.\ \sqrt{8}+2\sqrt{7}+\sqrt{6}$$ The OA is B. In this case, I just need to do the following, Can I say that the total time will be, Time of machine A + time of machine B, right? Then, $$T_A=\sqrt{8}+\sqrt{8-1}=\sqrt{8}+\sqrt{7}$$ And $$T_B=\sqrt{7}+\sqrt{7-1}=\sqrt{7}+\sqrt{6}$$ Finally, $$T_{total}=\left(\sqrt{8}+\sqrt{7}\right)+\left(\sqrt{7}+\sqrt{6}\right)=\sqrt{8}+2\sqrt{7}+\sqrt{6}$$ But, how can I get the combined time? I'm really confused by this PS question. Experts, any suggestion? Thanks in advance. Hi LUANDATO, Let's take a look at your question. The time required to complete a job is: $$=\sqrt{w}+\sqrt{\left(w-1\right)}$$ The rate is inverse of time, therefore we can find the rate as: $$Rate\ =\frac{1}{\sqrt{w}+\sqrt{\left(w-1\right)}}$$ Rationalizing the denominator: $$Rate\ =\frac{1}{\sqrt{w}+\sqrt{\left(w-1\right)}}\times\frac{\sqrt{w}-\sqrt{\left(w-1\right)}}{\sqrt{w}-\sqrt{\left(w-1\right)}}$$ $$Rate\ =\frac{\sqrt{w}-\sqrt{\left(w-1\right)}}{\left(\sqrt{w}+\sqrt{\left(w-1\right)}\right)\left(\sqrt{w}-\sqrt{\left(w-1\right)}\right)}$$ $$Rate\ =\frac{\sqrt{w}-\sqrt{\left(w-1\right)}}{w-\left(w-1\right)}$$ $$Rate\ =\frac{\sqrt{w}-\sqrt{\left(w-1\right)}}{w-w+1}$$ $$Rate\ =\frac{\sqrt{w}-\sqrt{\left(w-1\right)}}{1}$$ $$Rate\ =\sqrt{w}-\sqrt{\left(w-1\right)}$$ Since, Machine A weighs 8 pounds, therefore, rate of machine A is: $$Rate\ =\sqrt{8}-\sqrt{\left(8-1\right)}$$ $$Rate\ =\sqrt{8}-\sqrt{\left(7\right)}$$ Machine B weighs 7 pounds, therefore, rate of machine B is: $$Rate\ =\sqrt{7}-\sqrt{\left(7-1\right)}$$ $$Rate\ =\sqrt{7}-\sqrt{\left(6\right)}$$ Combined rate of Machine A and B is: $$Combined\ Rate\ =\left(\sqrt{8}-\sqrt{7}\right)+\left(\sqrt{7}-\sqrt{6}\right)$$ $$Combined\ Rate\ =\sqrt{8}-\sqrt{7}+\sqrt{7}-\sqrt{6}$$ $$Combined\ Rate\ =\sqrt{8}-\sqrt{6}$$ Now, we can find the time time taken by both the machines to finish the job by finding the reciprocal of the combined rate. $$Time=\frac{1}{\sqrt{8}-\sqrt{6}}$$ Rationalizing the denominator to simplify: $$Time=\frac{1}{\sqrt{8}-\sqrt{6}}\times\frac{\sqrt{8}+\sqrt{6}}{\sqrt{8}+\sqrt{6}}$$ $$Time=\frac{\sqrt{8}+\sqrt{6}}{8-6}$$ $$Time=\frac{\sqrt{8}+\sqrt{6}}{2}$$ Therefore, Option B is correct. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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