Question 48680: 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?
Multiple Choice:
A. A in 9 days, B in 1 day, and C in 8 days
B. A in 18 days, B in 24 days, and C in 14 2/5 days.
C. A in 20 1/2 days, B in 16 days, and C in 25 days.
D. A in 25 days, B in 12 2/3 days, and C in 28 days.
Found 2 solutions by stanbon, harshachittar:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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?
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A,B, C together DATA:
time = 6 days/job ; rate= 1/6 job/day
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B,C together DATA:
time = 9 days/job ; rate = 1/9 job/day
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A,C together DATA:
time = 8 days/job ; rate = 1/8 job/day
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EQUATIONS:
Let A = rate of A; B= rate= B; C=rate of C
A+B+C=1/6
B+C=1/9
A +C=1/8
Solve this system of equation to get:
A=1/8
B=1/24
C=5/72
Therefore:
A would take 8 days/job
B would take 24 days/job
C would take 14.4 days/job
Cheers,
Stan H.
Answer by harshachittar(3) (Show Source):
You can put this solution on YOUR website! Here goes,
The total time taken to complete the job by A + B + C is 6 days
The rate at which the total job is done can be represented as
A + B + C = 1/6 ----------------- Equ (1)
The total time taken to complete the job by B + C is 9 days
The rate at which the total job is done can be represented as
B + C = 1/9 ----------------- Equ (2)
The total time taken to complete the job by A + C is 8 days
The rate at which the total job is done can be represented as
A + C = 1/8 ----------------- Equ (3)
Solving the above Equ (1) and Equ (2) simultaneously for A we get,
A = 1/6 - 1/9
A = 1/18
Hence A would take 18 days to complete.
Solving the above Equ (1) and Equ (3) simultaneously for B we get,
B = 1/6 - 1/8
B = 1/24
Hence B would take 24 days to complete.
Replacing the value of B in Equ (2) we get
C = 1/9 - 1/24
C = 5/72
Hence B would take 14 2/5 days to complete.
So the correct answer from the Multiple choice is B.
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