SOLUTION: Harry can paint a house by himself in 6 days. His wife judy can paint the house by herself in x days. Write a rational expression F(x) that gives the portion of the house that they

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Harry can paint a house by himself in 6 days. His wife judy can paint the house by herself in x days. Write a rational expression F(x) that gives the portion of the house that they      Log On

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Question 365291: Harry can paint a house by himself in 6 days. His wife judy can paint the house by herself in x days. Write a rational expression F(x) that gives the portion of the house that they paint when working together for 2 days.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you add Harry's rate of working and Judy's rate of working,
you get their rate working together
given:
Harry's rate:
(1 house)/(6 days) = 1%2F6
Judy's rate:
(1 house)/(x days) = 1%2Fx
1%2F6+%2B+1%2Fx+=+%28x+%2B+6%29%2F%286x%29
This says that, working together, they can paint x+%2B+6
houses in 6x days
Or, what is the same thing, %28x+%2B+6%29%2F%286x%29 houses in 1 day
So, they will paint %282x+%2B+12%29%2F%286x%29+=+%28x+%2B+6%29%2F%283x%29 houses in 2 days
F%28x%29+=+%28x+%2B+6%29%2F%283x%29