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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 ## DS work rate problem ##### This topic has 2 expert replies and 0 member replies ## DS work rate problem ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult When working together at their constant rates, machines A and B can complete a certain task in 4 hours. How many hours would it take machine B to complete the task, when working alone at its constant rate? 1) When working alone at its constant rate, machine A can finish the task in 6 hours. 2) When working alone at their constant rates, it takes machine B 6 hours longer than machine A to finish the task OA: D ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 kyuhunl wrote: When working together at their constant rates, machines A and B can complete a certain task in 4 hours. How many hours would it take machine B to complete the task, when working alone at its constant rate? 1) When working alone at its constant rate, machine A can finish the task in 6 hours. 2) When working alone at their constant rates, it takes machine B 6 hours longer than machine A to finish the task $${T_{A \cup B}} = 4\,{\text{h}}$$ $$? = {T_B}\,\,\,\left[ {\text{h}} \right]$$ $$\left( * \right)\,\,\,\frac{1}{{{T_{A \cup B}}}} = \frac{1}{{{T_A}}} + \frac{1}{{{T_B}}}$$ $$\left( 1 \right)\,\,{T_A} = 6\,{\text{h}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\frac{1}{4} = \frac{1}{6} + \frac{1}{{{T_B}}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{T_B}\,\,{\text{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{SUFF}}.$$ $$\left( 2 \right)\,\,{T_B} = {T_A} + 6\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\frac{1}{4} = \frac{1}{{{T_A}}} + \frac{1}{{{T_A} + 6}}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\,{T_A} > 0\,\,{\text{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{T_B}\,\,{\text{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\text{SUFF}}.$$ $$\left( {**} \right)\,\,\,\,\frac{1}{4} = \frac{{2{T_A} + 6}}{{{T_A}\left( {{T_A} + 6} \right)}}\,\,\,\,\, \Rightarrow \,\,\,\, \ldots \,\,\,\, \Rightarrow \,\,\,\,{T_A}^2 - 2{T_A} - 24 = 0\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{roots}}\,\,{\text{product}}} \,\,\,\,\left( {\frac{c}{a} = } \right)\frac{{ - 24}}{1} < 0\,\,\,\, \Rightarrow \,\,\,\,{T_A} > 0\,\,{\text{unique}}$$ We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 kyuhunl wrote: When working together at their constant rates, machines A and B can complete a certain task in 4 hours. How many hours would it take machine B to complete the task, when working alone at its constant rate? 1) When working alone at its constant rate, machine A can finish the task in 6 hours. 2) When working alone at their constant rates, it takes machine B 6 hours longer than machine A to finish the task Statement 1: Case 1: Job = 12 units Since A and B together take 4 hours to complete the 12-unit job, the combined rate for A+B = 12/4 = 3 units per hour. Since A alone takes 6 hours to complete the 12-unit job, A's rate alone = 12/6 = 2 units per hour. B's rate = (combined rate for A+B) - (A's rate alone) = 3-2 = 1 unit per hour. Since B's rate = 1 unit per hour, B's time to complete the 12-unit job = 12/1 = 12 hours. Case 1: Job = 24 units Since A and B together take 4 hours to complete the 24-unit job, the combined rate for A+B = 24/4 = 6 units per hour. Since A alone takes 6 hours to complete the 24-unit job, A's rate alone = 24/6 = 4 units per hour. B's rate = (combined rate for A+B) - (A's rate alone) = 6-4 = 2 units per hour. Since B's rate = 2 units per hour, B's time to complete the 24-unit job = 24/2 = 12 hours. In each case, B's time alone is THE SAME : 12 hours. Thus, Statement 1 is SUFFICIENT. Statement 2: In Cases 1 and 2, B's time alone (12 hours) is 6 hours longer than A's time alone (6 hours). Implication: Statement 2 is conveying the same information as Statement 1. For B's time alone to be 6 hours longer than A's time alone, A's time alone must be 6 hours. Since Statement 1 is sufficient -- and Statement 2 conveys the same information as Statement 1 -- Statement 2 must also be SUFFICIENT. The correct answer is D. _________________ 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! 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