A work Problem

[avada]

Working alone, Printers X, Y, and Z can do a certain printing job, in 12, 15, and 18 hours respectively. What is the ratio of the time it takes printer x to do the job tot he time it takes printers Y and Z working together at their individual rates?
4/11
1/2
15/22
22/15
11/4
OG 22/15


The first thing I noticed was that it would take the printer working by himself longer so I eliminated answers 1 2 3. However I dont know how to do the math correctly to pick between the oteher two. I guessed correctly as 11/4 seemed to be too much time difference.

[GMATGuruNY]

Working alone, Printers X, Y, and Z can do a certain printing job, in 12, 15, and 18 hours respectively. What is the ratio of the time it takes printer x to do the job tot he time it takes printers Y and Z working together at their individual rates?
4/11
1/2
15/22
22/15
11/4

The time ratio for X:Y:Z = 12:15:18.
To make the math easier, divide all of the times by 3:
X:Y:Z = 4:5:6.

Let the job = the LCM of 4, 5, and 6 = 60.

X's rate = w/t = 60/4 = 15 pages per hour.
Y's rate = w/t = 60/5 = 12 pages per hour.
Z's rate = w/t = 60/6 = 10 pages per hour.
Combined rate for Y+Z = 12+10 = 22 pages per hour.

Rate and time are RECIPROCALS.
Since (rate for X alone) : (rate for Y+Z) = 15:22, (time for X alone) : (time for Y+Z) = 22:15.

The correct answer is D.

[bubbliiiiiiii]

Hi Mitch,

My approach is (1/x)/(1/y + 1/z) where x= 12, y=15 and z=18, and the equation yielded the reciprocal of correct answer.

Could you please let me know what is wrong in this approach?

[anuprajan5]

Pranay,

This is because you are taking the ratios of work rather than that of time.

X can do 1 job in 12 hours. Hence x can do 1/12 job in 1 hour.

When you take a ratio as you as you have done, you are taking the rato of work rather than the ratio of time.

Regards
Anup