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23 May 2022, 05:45
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Machine X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y working alone to complete the entire job?
A. 18
B. 16
C. 13 1/2
D. 12
E. 7 1/2
A. 18
B. 16
C. 13 1/2
D. 12
E. 7 1/2
genericUser
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23 May 2022, 07:08
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Machine X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y working alone to complete the entire job?
A. 18
B. 16
C. 13 1/2
D. 12
E. 7 1/2
ler \(\frac{1}{r}=\frac{1}{x}+\frac{1}{y}=\frac{1}{9}+\frac{1}{y}\) be the ration of the two machine combined
after the first 3 hours -> \(1 -\frac{1}{9}*3=\frac{2}{3}\)
after the remaining 4 hours -> \(\frac{2}{3} -\frac{1}{r}*4=0\) -> \(\frac{1}{r}=\frac{1}{6}\)
\(\frac{1}{6}=\frac{1}{9}+\frac{1}{y}\) -> \(\frac{1}{y}=\frac{1}{18}\)
A. 18
B. 16
C. 13 1/2
D. 12
E. 7 1/2
ler \(\frac{1}{r}=\frac{1}{x}+\frac{1}{y}=\frac{1}{9}+\frac{1}{y}\) be the ration of the two machine combined
after the first 3 hours -> \(1 -\frac{1}{9}*3=\frac{2}{3}\)
after the remaining 4 hours -> \(\frac{2}{3} -\frac{1}{r}*4=0\) -> \(\frac{1}{r}=\frac{1}{6}\)
\(\frac{1}{6}=\frac{1}{9}+\frac{1}{y}\) -> \(\frac{1}{y}=\frac{1}{18}\)
23 May 2022, 07:15
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Bunuel
Machine X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y working alone to complete the entire job?
A. 18
B. 16
C. 13 1/2
D. 12
E. 7 1/2
A. 18
B. 16
C. 13 1/2
D. 12
E. 7 1/2
Boy, wouldn't it be nice if we knew what the job is? It's really common on rates questions to be able to make your life easier by just making up what the job is.
Let's make the job solving 9 GMAT questions. X can solve 9 GMAT questions in 9 hours. X works alone for 3 hours, so it does 3 GMAT questions. Over the next four hours, X an Y work together to finish the remaining 6 GMAT questions. In those 4 hours, X would be able to complete 4 more questions, which means Y completed the other 2. Y did 2 questions in 4 hours, so Y does 1 question every 2 hours. The question asks us how long it would take Y to complete 9 GMAT questions on its own. Since it does 1 question every 2 hours, it will take 18 hours to complete 9 questions.
Answer choice A.
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