SOLUTION: Beth, Bill, and Edie, can paint a house together in 10 hours. BIll and Edie together can paint the same house in 15 hours. One day, all three worked on the same kind of house for 4

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Beth, Bill, and Edie, can paint a house together in 10 hours. BIll and Edie together can paint the same house in 15 hours. One day, all three worked on the same kind of house for 4      Log On


   

Question 537263: Beth, Bill, and Edie, can paint a house together in 10 hours. BIll and Edie together can paint the same house in 15 hours. One day, all three worked on the 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 richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Beth=h
Bill=b
Edie=d
10/h+10/b+10/d=1
15/b+15/d=1
4/h+4/b+4/d+8/h+8/b=1
b=24
d=40
h=30
check
10/30+10/24+10/40=1
40+50+30/120=1
120/120=1
ok
15/24+15/40=1
5/8+3/8=1
8/8=1
ok
4/30+4/24+4/40+8/30+8/24=1
(16+20+12)/120+4/15+4/12=1
4/10+4/15+1/3=1
2/5+4/15+5/15
(6+4+5)/15=1
15/15=1
ok