BTW --work problems are just one of those you should know the formula to solving for time (TIME A * TIME B divided by TIME A + TIME B) when given discrete simultaneous rates. Read up on this because it will save you a bunch of time from trying to figure out what the heck will be going on with which rate etc. It's kinda like triangle problems. You will eventually solve them but you really should not be inventing the wheel during the test. I think the GMAT just wants you to be able to recognize which type of problem you are working with and apply very simple mathematics.

rate o x= 1/12
rate of y and z combined = 1/15+1/18 = 33/15.18

ratios is

22/15

option is D

c

The answer is D.

D 22/15

D 22/15

X does 1/12th of work in an hour.
Y+Z together do 1/18 and 1/15 of work together in an hour.
Simplifying they both together do 11/90 th of work.
Therefore they will complete the work in 90/11 if they work together

now the ratio asked is (12*11)/90---->22/15

22/15
Just reverse the time to rate for Y & Z. add the rates 1/y+1/z
Then reciprocal of 1/y and 1/x gives time taken by y and z together to complete the job..
Thats it..Ans = time taken by x/time taken by y and z together.

ANSWER: D

22/15

The answer is D.
However, I got it wrong. Thought it to be C.
Thought we had to find the ratio of rates and not the total time!

Key Takeaway: *Read* the question! X-(

Correct answer is definitely D

Work done by x in 1 hour = 1/12
Work done by y and z in 1 hour = 1/15+1/18=11/90

so total time taken by both to complete the job =90/11 hrs

time taken by x /time taken by a & b = 18/(90/11)=22/15

resilient wrote:working alone, printers x,y, and z can do a certain printing job, consisitning of a large number of pages, 12, 15, and 18 hours, respectively. 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, working together at their individual rates?

a. 4/11
b.1/2
c. 15/22
d.22/15
e.11/4

qa is d. I dont see why C is wrong. I dont see why the solution flips the combined rate of y and z working together. help stuart?

Answer is 22/15

Best way to save time on such problems is to remove the fraction part by assuming the work as a LCM of the time taken to complete the work and then find individual work done/unit time. This has been explained earlier by Farooq.

Working with numbers definitely saves time when compared to working with fractions

Let us say the printer needs to print 180 pages.
Then,
the rate at which printer x works => 180/12 => 15 pages/hr
the rate at which printer y works => 180/15 => 12 pages/hr
the rate at which printer z works => 180/18 => 10 pages/hr
the rate at which printers y and z work => 10+12 => 22 pages/h

ratio of time taken by printer x to printer y and z together => (180/15)/(180/22) => 22/15