SOLUTION: A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man work

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Question 384732: A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job?
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Since we must solve for 3 unknowns, we must come up with 3 separate equations.
let x = number of hours A can complete the job alone.
let y = number of hours B can complete the job alone.
let z = number of hours C can complete the job alone.
A's rate =1/x
B's rate = 1/y
C's rate = 1/z
sum of individual hourly rates = hourly rate when individuals work together
1/x + 1/y +1/z =1/6
1/y + 1/z = 1/9
1/x +1/z = 1/8
1/y =1/9 -1/z
1/x =1/8-1/z
1/8-1/z +1/9-1/z+1/z=1/6
-1/z = 1/6 -1/8 -1/9
-1/z = 12/72 -9/72-8/72 =-5/72
1/z = 5/72 = 1/14.4
1/y = 8/72 -5/72 =3/72 =1/24
1/x = 9/72 -5/72 =4/72 =1/18
ans: A can do the job working alone in 18 hours
B can do the job working alone in 24 hours
C can do the job working alone in 14.4 hours