Ratio - Completing a Job Working Alone

[Jackie9988]

I have the answer to a math problem, but I have two questions.
1) Why do I need to INVERT 11/90 to 90/11?
2) Why do I use "12" for printer X instead of "1/12?"

Working alone, printer 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

From the given information, it can be stated that printer Y can do 1/15 of the job per hour, and printer Z can do 1/18 of the job per hour. Together, printers Y and Z can do 11/90 of the job per hour.

1/15 + 1/18 = 6/90 + 5/90 = 11/90

In turn that it takes them 90/11 hours to complete the job. It is given that printer X complete the job in 12 hours. Therefore, the ratio of the time required for X to do the job to the time required for Y and Z working together to do the job is:


12 / 90/11 = 12 • 11/90 = 2 • 11/15 = 22/15

Answer: D

 

[galactus]

You are correct. Good work.

 

[stapel]

1) Why do I need to INVERT 11/90 to 90/11?

If you can do one-third of a job in an hour, how many hours will it take to complete one job?

If you can do one-fifth of a job in an hour, how many hours will it take to complete one job?

If you can do eleven-ninetieths of a job in an hour, how many hours will it take to complete one job?

2) Why do I use "12" for printer X instead of "1/12?"

Where do you mean? You are given that X takes twelve hours so, for "the time to complete the job", you have to use "12".

It sounds like you haven't yet studied this sort of word problem. (The questions you've asked indicate that you probably don't fully understand the easy examples, which is making this more-complex example utterly befuddling.) Try studying this lesson on the topic. :wink:

Eliz.