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Three machines X, Y, and Z operate independently of one another. [#permalink]
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Updated on: 03 Apr 2018, 13:26
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Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y? A) 1 3/5 B) 3 C) 3 3/7 D) 5 1/4 E) 17 3/5
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Originally posted by OCDianaOC on 03 Apr 2018, 12:50.
Last edited by OCDianaOC on 03 Apr 2018, 13:26, edited 1 time in total.



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Re: Three machines X, Y, and Z operate independently of one another. [#permalink]
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03 Apr 2018, 13:20



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Re: Three machines X, Y, and Z operate independently of one another. [#permalink]
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03 Apr 2018, 13:26
Bunuel wrote: OCDianaOC wrote: Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in hours. What is the value of y?
A) 1 3/5 B) 3 C) 3 3/7 D) 5 1/4 E) 17 3/5 Please edit the highlighted part: 8/5 hours? Thank you. Edited! Thanks, didn't realize it didn't paste over at first.



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Three machines X, Y, and Z operate independently of one another. [#permalink]
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03 Apr 2018, 15:30
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OCDianaOC wrote: Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?
A) 1 3/5 B) 3 C) 3 3/7 D) 5 1/4 E) 17 3/5 One approach, \(R*T = W\): find combined rate; add rates to solve for Y's rate; and use Y's rate to find Y's time GivenRates are in \(\frac{Jobs}{hour}\)X's rate = \(\frac{1}{12}\)Y's rate = \(\frac{1}{Y}\)Z's rate = \(\frac{1}{4}\)TIME all three machines take, working together, to finish the job = \(1\frac{3}{5}hrs=\frac{8}{5}\) hours Combined RATE?\(R*T = W\), so \(R=\frac{W}{T}\)All three, RATE = \(\frac{1}{(\frac{8}{5})}=(1*\frac{5}{8})=\frac{5}{8}\)Add rates, solve for Y's rate: (\(\frac{1}{X}+\frac{1}{Y}+\frac{1}{Z})=(\frac{1}{12}+\frac{1}{Y}+\frac{1}{4})=\frac{5}{8}\)
\((\frac{5}{8}\frac{1}{4}\frac{1}{12})=\frac{1}{Y}=(\frac{15}{24}\frac{6}{24}\frac{2}{24})=\frac{7}{24}\)Y's TIME?\(\frac{7}{24}\) is Y's rate. The job is 1 Rate and time are inversely proportional. Flip Y's rate fraction to get Y's time*: \(\frac{24}{7}hrs=3\frac{3}{7}hrs\)Answer C * \(R*T=W\), so \(T=\frac{W}{R}\) \(W = 1\) \(T =\frac{1}{(\frac{7}{24})}=(1 * \frac{24}{7})=(\frac{24}{7})=3\frac{3}{7}\)hrs
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Re: Three machines X, Y, and Z operate independently of one another. [#permalink]
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03 Apr 2018, 17:52
The Total work can be assumed to be 120 (LCM of (time taken to complete the job) 12,4,8/5 (ignore the denominator )) =120 units This will make the calculation quite easier. Now No of units of works done by X per hour = \(120/12 =10\) No of units of works done by Z per hour = \(120/4 =30\) No of units of works done per hour by all three of them = \(120/(8/5) =75\) Thus work done by Y per hour = work done by all three  (work done by X +work done by Z) =75(10+30) =35 Hence the time taken by Y to complete the work = 120/35 = 24/7 = 3 3/7 = Answer = C OCDianaOC wrote: Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?
A) 1 3/5 B) 3 C) 3 3/7 D) 5 1/4 E) 17 3/5
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Re: Three machines X, Y, and Z operate independently of one another. [#permalink]
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03 Apr 2018, 22:21
OCDianaOC wrote: Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?
A) 1 3/5 B) 3 C) 3 3/7 D) 5 1/4 E) 17 3/5 1/y=[1/(8/5)(1/4+1/12)] y=24/7=3 3/7 hours C



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Re: Three machines X, Y, and Z operate independently of one another. [#permalink]
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03 Apr 2018, 23:16
Bunuel wrote: OCDianaOC wrote: Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in hours. What is the value of y?
A) 1 3/5 B) 3 C) 3 3/7 D) 5 1/4 E) 17 3/5 Please edit the highlighted part: 8/5 hours? Thank you. X can complete the work in 1/12 hours Y can complete the work in 1/ x hours Z can complete the work in 1/4 hours Together they can complete the work in 5/8 hours So 1/12+1/x+1/4=5/8 1/x=5/81/3 1/x=7/24 X=24/7 which is 3 3/7 Sent from my SMG925I using GMAT Club Forum mobile app



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Re: Three machines X, Y, and Z operate independently of one another. [#permalink]
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06 Apr 2018, 08:47
OCDianaOC wrote: Three machines X, Y, and Z operate independently of one another. Machine X working alone can complete a job in 12 hours, machine Y working alone can complete the job in y hours, machine Z working alone can complete the job in 4 hours, and all three machines working together and independently can complete the job in 1 3/5 hours. What is the value of y?
A) 1 3/5 B) 3 C) 3 3/7 D) 5 1/4 E) 17 3/5 The rate of machine X is 1/12, the rate of machine Y is 1/y, and the rate of machine Z is 1/4. Since the 3 machines can complete the job in 1 3/5 = 8/5 hours, we can create the following equation for the combined rate of the 3 machines: 1/12 + 1/y + 1/4 = 1/(8/5) 1/12 + 1/y + 1/4 = 5/8 Multiplying by 24y, we have: 2y + 24 + 6y = 15y 24 = 7y 24/7 = 3 3/7 = y Answer: C
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