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Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11 (B) 1/2 (C) 15/22 (D) 22/15 (E) 11/4

Problem Solving Question: 130 Category:Arithmetic Operations on rational numbers Page: 78 Difficulty: 600

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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
05 Mar 2014, 01:17

Expert's post

SOLUTION

Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11 (B) 1/2 (C) 15/22 (D) 22/15 (E) 11/4

The rate of Y and Z are 1/15 and 1/18 job/hour, respectively.

Their combined rate is 1/15 + 1/18 = 1/t. Thus the time it takes Printers Y and Z to do the job is t = 90/11.

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
08 Mar 2014, 11:38

Expert's post

SOLUTION

Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?

(A) 4/11 (B) 1/2 (C) 15/22 (D) 22/15 (E) 11/4

The rate of Y and Z are 1/15 and 1/18 job/hour, respectively.

Their combined rate is 1/15 + 1/18 = 1/t. Thus the time it takes Printers Y and Z to do the job is t = 90/11.

Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
18 Mar 2014, 03:14

Rate(X)=1/12 Rate(Y)=1/15 Rate(Z)=1/18

Time for X=12

Combined Rate of Y and Z= 1/15 + 1/18 = 33/(18*15)

Since Rate * Time = work

And work =1 then Time for combined Y and Z = (18*15)/33

Ratio of Time for X/Time for combined Y and Z

(12*33)/(18*15)=22/15

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Re: Working alone, Printers X, Y, and Z can do a certain printin [#permalink]
15 Apr 2014, 20:10

Printer X can do Printing Job in 12 hrs. So Printer X completes (1/12)th of the work in 1hr.

Printer Y can do Printing Job in 15 hrs. So Printer Y completes (1/15)th of the work in 1hr.

Printer Z can do Printing Job in 18 hrs. So Printer Z completes (1/18)th of the work in 1hr.

Printer's Y and Z combined rate(working for 1 hr) is 1/15+1/18 = 11/90;

ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates is (1/12)/(11/90) = 15/22;

so rate is 15/22; rate is inversly proportional to time. Time is 22/15; Hence D