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 working al

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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 working al      Log On

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Question 197922: 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 josmiceli(6786) About Me  (Show Source):
You can put this solution on YOUR website!
I will say the following:
A's rate of working is (1 job)/(a days)
B's rate of working is (1 job)/{b days)
C's rate of working is (1 job)/(c days)
---------------------------------------
I can add their rates of working to get a
rate at which they work together
(1) 1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F6
(2) 1%2Fb+%2B+1%2Fc+=+1%2F9
(3) 1%2Fa+%2B+1%2Fc+=+1%2F8
-------------------------
From (2)
1%2Fb+=+1%2F9+-+1%2Fc
From (3)
1%2Fa+=+1%2F8+-+1%2Fc
Substitute these into (1)
(1) 1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F6
1%2F8+-+1%2Fc+%2B+1%2F9+-+1%2Fc+%2B+1%2Fc+=+1%2F6
1%2F8+%2B+1%2F9+-+1%2Fc+=+1%2F6
1%2Fc+=+1%2F8+%2B+1%2F9+-+1%2F6
Multiply both sides by 72c
72+=+9c+%2B+8c+-+12c
5c+=+72
c+=+14.4
From (2)
(2) 1%2Fb+%2B+1%2Fc+=+1%2F9
1%2Fb+%2B+5%2F72+=+1%2F9
72+%2B+5b+=+8b
3b+=+72
b+=+24
From (3)
(3) 1%2Fa+%2B+1%2Fc+=+1%2F8
1%2Fa+%2B+5%2F72+=+1%2F8
72+%2B+5a+=+9a
4a+=+72
a+=+18
A can do the job in 18 days
B can do the job in 24 days
C can do the job in 14.4 days
check answer:
(1) 1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F6
1%2F18+%2B+1%2F24+%2B+1%2F14.4+=+1%2F6
Multiply both sides by 72
4+%2B+3+%2B+5+=+12
12+=+12
OK
(2) 1%2Fb+%2B+1%2Fc+=+1%2F9
1%2F24+%2B+1%2F14.4+=+1%2F9
Multiply both sides by 72
3+%2B+5+=+8
8+=+8
OK
(3) 1%2Fa+%2B+1%2Fc+=+1%2F8
1%2F18+%2B+1%2F14.4+=+1%2F8
Multiply both sides by 72
4+%2B+5+=+9
9+=+9
OK