SOLUTION: Sam can do a certain job in six days. After working alone for three days, he is joined by Katy, and together they finish the work in one more day. How long would it take Katy alone

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Sam can do a certain job in six days. After working alone for three days, he is joined by Katy, and together they finish the work in one more day. How long would it take Katy alone      Log On


   

Question 623852: Sam can do a certain job in six days. After working alone for three days, he is joined by Katy, and together they finish the work in one more day. How long would it take Katy alone?
Answer by lwsshak3(11628) About Me  (Show Source):
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Sam can do a certain job in six days. After working alone for three days, he is joined by Katy, and together they finish the work in one more day. How long would it take Katy alone?
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let x=how long it would take for Katy to do the job alone
1/x=Katy's work rate
1/6=Sam"s work rate
sam worked 4 days
katy worked one day
worked done=work rate*time on job
4(1/6)+1(1/x)=100% of the job
4/6+1/x=1
1/x=1-4/6=1-2/3=1/3
x=3
how long would it take for Katy to do the job alone=3hours