prude_sb wrote:
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
----ASIDE-----------------------------------
For work questions, there are two useful rules:
Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobExample: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour
Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire jobExample: If Sam can complete 1/8 of the job
in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
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Let’s use these rules to solve the question. . . .
Printer Y takes 15 hours to complete a job. So, by rule #1, printer Y’s rate is 1/15 of the job
per hourPrinter Z takes 18 hours to complete a job. So, by rule #1, printer Z’s rate is 1/18 of the job
per hourSo, their combined rate per hour = 1/15 + 1/18
= 6/90 + 5/90
=
11/90So, working together, printers Y and Z can complete the
11/90 of the job
in one hour.
When we apply rule #2, we can conclude that, working together, printers Y and Z will complete the entire job in
90/11 hours.
What is the ratio of the time it takes printer X to do the job, working at its rate, to time it takes printers y and z to do the job?So, (time for X to complete)/ (time for Y & Z to complete) = 12/(
90/11)
= (12)(11/90)
= 22/15
Answer: D