SOLUTION: Hi, I was hoping I could get some help... Sara takes 3 hours longer to paint a floor than it takes Katie. When they work together, it takes them 2 hours.How long would each take t

Question 136978: Hi, I was hoping I could get some help...
Sara takes 3 hours longer to paint a floor than it takes Katie. When they work together, it takes them 2 hours.How long would each take to do the job alone?
So far I have
Sara=X+3
Kate=X
(2/X+3 + 2/X = 1) all that multiplied by X(X+3)
But I don't know what to do next, or even if that is right
Thank you for the help
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
SORRY SORRY SORRY. i MISREAD THE PROBLEM AND USED SARA'S TIME AS 3 TIMES kATIE INSTEAD OF 3 HOURS LONGER.
the formula for working together is:
x*y/(x+y) time working together.
Sara=k+3
Katie=k
K(K+3)/(K+3+K)=2
(K^2+3K)/(2K+3)=2
K^2+3K=2(2K+3)
K^2+3K=4K+6
K^2+3K-4K-6=0
K^2-K-6=0
(K-3)(K+2)
K-3=0
K=3 HOURS FOR KATIE WORKING ALONE.
3+3=6 HOURS FOR SARA WORKING ALONE.

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