SOLUTION: I'm stuck on this and need help,....Alfred and Bill working together can paint a house in 24 days. If Alfred can only do 2/3 as much work as Bill, how long would it take each of th

Algebra ->  Rate-of-work-word-problems -> SOLUTION: I'm stuck on this and need help,....Alfred and Bill working together can paint a house in 24 days. If Alfred can only do 2/3 as much work as Bill, how long would it take each of th      Log On


   

Question 1026725: I'm stuck on this and need help,....Alfred and Bill working together can paint a house in 24 days. If Alfred can only do 2/3 as much work as Bill, how long would it take each of them to paint the house by themselves?
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
Alfred's rate is 1 house per x days or 1/x house per day.
Bill's rate is 1 house per y days or 1/y house per day.

If Alfred can only do 2/3 as much work as Bill
So 1/x = (2/3)(1/y)

or 1/x = 2/(3y)

Alfred and Bill working together can paint a house in 24 days. 
Their combined rate is 1/x + 1/y house per day.

their combined rate times 24 days = 1 house painted. So

(24)(1/x+1/y) = 1 house painted

So we have the system of equations:

system%281%2Fx+=+%282%2F3%29%281%2Fy%29%2C%2824%29%281%2Fx%2B1%2Fy%29+=+1%29

Simplifying

system%281%2Fx+=+2%2F%283y%29%2C1%2Fx%2B1%2Fy+=+1%2F24%29


Substitute 2/(3y) for 1/x in the second equation:

2%2F%283y%29%2B1%2Fy%29+=+1%2F24%29

2%2F%283y%29%2B3%2F%283y%29+=+1%2F24%29

5%2F%283y%29+=+1%2F24%29

3y=24%2A5

Divide both sides by 3

y=8%2A5

y=40

Substitute in 

1%2Fx%2B1%2Fy+=+1%2F24

1%2Fx%2B1%2F40+=+1%2F24

Multiply through by LCD = 120

120%2B3x+=+5x

120=2x

60=x

Edwin