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 it will take 8 days. In how many days can each man working alone

Algebra ->  College  -> Linear Algebra -> 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 it will take 8 days. In how many days can each man working alone      Log On


   

Question 126265: 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 it will take 8 days. In how many days can each man working alone do the job?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a = time A takes
b = time B takes
c = time C takes
The sum of their rates is the final rate
1 job/a days + 1 job/b days + 1 job/c days = 1 job/6 days
1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F6
also given is
1%2Fb+%2B+1%2Fc+=+1%2F9
and
1%2Fa+%2B+1%2Fc+=+1%2F8
I need to find a, b, andc
I can directly substitute 1%2Fb+%2B+1%2Fc+=+1%2F9
into 1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F6
1%2Fa+%2B+1%2F9+=+1%2F6
1%2Fa+=+1%2F6+-+1%2F9
1%2Fa+=+3%2F18+-+2%2F18
1%2Fa+=+1%2F18
a+=+18 answer
substituting,
1%2Fa+%2B+1%2Fc+=+1%2F8
1%2F18+%2B+1%2Fc+=+1%2F8
1%2Fc+=+1%2F8+-+1%2F18
1%2Fc+=+9%2F72+-+4%2F72
1%2Fc+=+5%2F72
c+=+14.4 answer
1%2Fb+%2B+1%2Fc+=+1%2F9
1%2Fb+%2B+1%2F%2872%2F5%29+=+1%2F9
1%2Fb+%2B+5%2F72+=+1%2F9
1%2Fb+=+1%2F9+-+5%2F72
1%2Fb+=+8%2F72+-+5%2F72
1%2Fb+=+3%2F72
b+=+24 answer
A takes 18 days working alone, B takes 24 days working alone
and C takes 14.4 days working alone
check answers:
1%2Fa+%2B+1%2Fb+%2B+1%2Fc+=+1%2F6
1%2F18+%2B+1%2F24+%2B+1%2F%2872%2F5%29+=+1%2F6
4%2F72+%2B+3%2F72+%2B+5%2F72+=+12%2F72
12%2F72+=+12%2F72
OK