SOLUTION: Three workers are named X ,Y,and Z. Suppose that together X and Y and can do a job in 4 hours, X and Z can do it in 6 hours, and X,Y and Z can do the job in 3 hours. How many hours

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Three workers are named X ,Y,and Z. Suppose that together X and Y and can do a job in 4 hours, X and Z can do it in 6 hours, and X,Y and Z can do the job in 3 hours. How many hours      Log On


   

Question 315892: Three workers are named X ,Y,and Z. Suppose that together X and Y and can do a job in 4 hours, X and Z can do it in 6 hours, and X,Y and Z can do the job in 3 hours. How many hours will Y alone need to do the job?
A) 6hrs B) 8hrs C) 10 hrs D) 12 hrs
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's first find the hourly rate of each group:
If X+Y can do the job in 4 hours, then they can do 1%2F4 of the job in 1 hour.
If X+Z can do the job in 6 hours, then they can do 1%2F6 of the job in 1 hour.
If X+Y+Z can do the job in 3 hours, then they can do 1%2F3 of the job in 1 hour.
These can be expressed as:
1) X%2BY+=+1%2F4
2) X%2BZ+=+1%2F6
3) X%2BY%2BZ+=+1%2F3
Express the first 2 equations in terms of X.
1a) Y+=+%281%2F4%29-X
2a) Z+=+%281%2F6%29-x Now substitute these for Y and Z in equation 3) to get:
3a) X%2B%28%281%2F4%29-X%29%2B%28%281%2F6%29-X%29+=+1%2F3 Simplify and solve for X.
X+=+1%2F12
To find the hourly rate of Y, subtract X+=+1%2F12 from equation 1).
X%2BY+=+1%2F4-X+=+1%2F12
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Y+=+1%2F6 This is the hourly rate of Y, so it will take Y 6 hours to complete the job.