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Question 377051: Three painters, Beth, Bill, and Edie working together can paint a home in 10 hours. Bill and Edie together have painted a similiar house in 15 hours. One day, all three worked on this same kind of house for 4 hours, after which Edie left. Beth and Bill required 8 more hours to finish. Assuming no gain or loss in efficiency, how long should it take each person to complete such a job alone?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! let x = hours Beth can do the job alone
let y = hours Bill can do the job alone
let z = hours Ed can do the job alone
equating hourly rates,
1/x + 1/y +1/z = 1/10
1/y +1/z = 1/15
12/x +12/y +4/z =1 (Beth and Bill worked 12 hours while Ed only worked 4 hours to complete 100% of the job.)
1/z = 1/15-1/y, 1/y=1/15-1/z
1/x +1/y +1/15-1/y=1/10
1/x =1/10-1/15=3/30-2/30=1/30
x=30
12/30+12/y +4*(1/15-1/y)=1
12/30+12y+4/15-4/y =1
8/y=1-12/30-4/15=30/30-12/30-8/30=10/30=1/3
y=24
1/z=1/15-1/y=1/15-1/24=16/240-10/240=6/240=1/40
z=40
ans: Beth can do the job alone in 30 hours
Bill can do the job alone in 24 hours
Ed can do the job alone in 40 hours
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