I don't add much to what already has been said, but here i go anyways. I like to represent the rates on this way:

Time * Rate = Work:

12 * (1/x) = 1 hence x = 12
15 * (1/y) = 1 hence y =15
18 * (1/z) = 1 hence z = 18

The rate of machine Y and Z combined is:

1/15 + 1/18 (respectively)
33/270
11/90

The time it takes Y and Z to make the work is:

T * (11/90) = 1
T = 90/11

To ratio from X to (Y+Z) to do the work is:

12/(90/11)
12 * (11/90)
22/15

Correct Answer: [spoiler](D)[/spoiler]

Ans is D 22/15.

Time taken by Y,Z working together: 1/(1/15+1/18) = 90/11

Ratio of x/(y+z) = 12/(90/11) = 22/15

Using the 1/t formula, I got D.

However plugging in some value is also a very good way to solve it in a faster and easier way!

Collective study rocks!

Let work be defined as "W" , say it is total no. of pages

Rate of X doing work W = W/12

Rate of Y doing work W = W/15

Rate of Y doing work W = W/18

time for X to finish work W = W/(W/12) = 12

time for Y & Z together to finish work W = W/(combined rate of Y & Z) = W/((W/15)+(W/18)) = 90/11

ratio of times from above = 12/(90/11) = 22/15

Answer is
D. 22/15

Answer C ?15/22

Ok I guess I got excited there . Its D as obviously as X alone will take more time than Y & Z combined. C was a trap answer, fell for it

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?

You have done the right method and gotten the right answer. However, you have solved the problem in terms of the rates and the question asks for the time which is always the inverse of the rate. All other solutions are great but this is the piece you are missing as to why it is not see

Remember W (work) = RT and if someone takes 8 hours to do a job that means that are doing 1/8 of the job per hour. So rate is always the inverse of time.

This is why D is correct

IMO - D

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?

Noticeably printer x takes 12 hours to do the job, and printers y and z working together would take 15 × 18/ (15 + 18) hours to do the same job; the required ratio would hence be

12 : 15 × 18/ (15 + 18) solving we get it as [spoiler]22:15

D

Catch: Order matters in answering a ratio, ratio a to b is not same as ratio b to a.[/spoiler]

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?

Let the total work be 180 units ( LCM of 12, 15, 18 )

Thus

x produces 15 units/ hour

y produces 12 units/ hour

z produces 10 units / hour


Thus work done by both X & Y in one hour is 22 units

X produces 15 units per hour .

So 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 is


15 / 22

Since we're asked for a proportion, only the relative values matter. Each printer's rate is a multiple of 3, so we can reduce the rates for x, y, and z to be 4, 5, and 6, respectively.

Formula for combined work when you have two (people, machines, etc.) working together is:

yz / (y + z)

So combined rate of y and z equals:

5(6) / (5 + 6) or 30 / 11

Now create the ratio:

4 / (30 /11) or 4(11/30) or 2(11/15) = 22/15 (d)

Answer D: Based on 12/15/18 => 1< the ratio < 2 => the ratio = 22/15

d.

we know it is 12/h. where h < 15 and 18. so answers a,b,e are out.

leaves c and d .

c < 1 so not likely.

answer is then d.

or do the math. which i see on the other answers. my answer is done in 15 seconds. the math takes just 45 seconds or so. one should do the math to be sure on a question like this. but my answer is fast.

farooq wrote:

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?

Lets say total no. of pages that each printer prints are 180.

X prints 180 pages in 12 hours. 15 pages per hour.
Y prints 180 pages in 15 hours. 12 Pages per hour.
Z prints 180 pages in 18 hours. 10 pages per hour.

If Y and Z both work together, they will print 12+10 = 22 pages per hour.

Therefore total no. of hours to print 180 pages by Y and Z will be 180/22.

Time taken by X to print total no. of pages/Time taken by (Y and Z together)to print total no. of pages = 12/(180/22) = 22/15

Farooq, the pick a number strategy is quite elegant. My only question is how can one easily and quickly pick a mumber, in this case 180. Is there a method to picking a number?