Question 12375: 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. How many days will it take each man to do the job alone?
A. A in 9 days, B in 1 day, and C in 8 days
B. A in 25 days, B in 12 2/3 day, and C in 28 days
C. A in 20 1/2 days, B in 16 day, and C in 25 days
D. A in 18 days, B in 24 day, and C in 14 2/5 days
I don't have a clue where to begin with this problem. I would appreciate any help--thanks
Answer by AnlytcPhil(1810)   (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. How many days will it take each man
to do the job alone?
A. A in 9 days, B in 1 day, and C in 8 days
B. A in 25 days, B in 12 2/3 day, and C in 28 days
C. A in 20 1/2 days, B in 16 day, and C in 25 days
D. A in 18 days, B in 24 day, and C in 14 2/5 days
I don't have a clue where to begin with this problem. I would
appreciate any help--thanks
Let x = the number of days it would take A to do 1 job alone.
Let y = the number of days it would take B to do 1 job alone.
Let z = the number of days it would take C to do 1 job alone.
Make this chart:
Number of jobs | Rate(jobs/days) | Time(days)
A alone | |
B alone | |
C alone | |
A,B,& C | |
B & C only | |
A & C only | |
In each case 1 job was done, so fill in 1 for each of the
numbers of jobs
Number of jobs | Rate(jobs/days) | Time(days)
A alone 1 | |
B alone 1 | |
C alone 1 | |
A,B,& C 1 | |
B & C only 1 | |
A & C only 1 | |
Now fill in the times (numbers of days.
Number of jobs | Rate(jobs/day) | Time(days)
A alone 1 | 1/x | x
B alone 1 | 1/y | y
C alone 1 | 1/z | z
A,B,& C 1 | 1/6 | 6
B & C only 1 | 1/9 | 9
A & C only 1 | 1/8 | 8
Now fill in the rates using rate = (jobs done)/(time)
The rate for A,B,& C equals the sum of their individual
rates, which must equal 1/6, so
1/x + 1/y + 1/z = 1/6
The rate for A & C equals the sum of their individual rates,
which must equal 1/8, so
1/x + 1/z = 1/8
The rate for B & C equals the sum of their individual rates,
which must equal 1/9, so
1/y + 1/z = 1/9
So we have this system of equations:
1/x + 1/y + 1/z = 1/6
1/x + 1/z = 1/8
1/y + 1/z = 1/9
Don't clear of fractions, but solve for 1/x, 1/y, and 1/z.
Can you do this system? If not, post again and ask how to solve it.
You'll get 1/x = 1/18, 1/y = 1/24, and 1/z = 5/72, which
means x = 18 days, y = 24 days, z = 72/5 or 14 2/5 days, and the
correct choice is D.
Edwin
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