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

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) (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:



Simplifying




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









Divide both sides by 3





Substitute in 





Multiply through by LCD = 120







Edwin

RELATED QUESTIONS
Alfred, Mindy, and Casey can mow their lawn in 60 minutes if they work together. If it... (answered by josgarithmetic,richwmiller,stanbon)

BILL CAN PAINT A HOUSE IN 2 DAYS, GEORGE CAN PAINT THE SAME HOUSE IN 3 DAYS, AND JEFF... (answered by addingup)

Jose paints a wall in 5 days. If Jose and Alfred works together fot at most 2 days, what... (answered by fractalier)

Bill can paint a house in 5 days and Samantha can paint the same house in 7 days. How... (answered by ankor@dixie-net.com)

Three friends, Alfred, Bianca, and Carlos, decide to buy a car. Alfred pays � of the... (answered by solver91311)

If one painter can paint a house in 8 days and another painter can paint the same house... (answered by richwmiller,jsmallt9)

If bill can paint a house in 4 hours and joe can paint a house in 6 hours, how long would (answered by unlockmath,eric.schuh)

Hello, I am taking some practice test for the College placement test and I am having... (answered by longjonsilver)

A man can paint a certain house in 5 days. He and his brother can do the job together in... (answered by josgarithmetic,ikleyn)