SOLUTION: A can do a piece of work in 36 days, B in 54 days and C in 72 days. All of them began together but A left 8 days and B left 12 days before the completion of the work. How many days

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Question 230488: A can do a piece of work in 36 days, B in 54 days and C in 72 days. All of them began together but A left 8 days and B left 12 days before the completion of the work. How many days in all did C put in till the entire work was finished?

Found 2 solutions by stanbon, scott8148:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A can do a piece of work in 36 days,--------A's rate is 1/36 job/day
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B in 54 days -------------------------------B's rate is 1/54 job/day
C in 72 days.-------------------------------C's rate is 1/72 job/day
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All of them began together but A left 8 days and B left 12 days before the completion of the work. How many days in all did C put in till the entire work was finished?
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Equation:
Let x be the number of days required to do the job:
(x-8)(1/36)+(x-12)(1/54)+x(1/72) = 1 job
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I'll let you solve that for "x" which is how many days C worked.
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Cheers,
Stan H.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x = "total days to complete work"

(x - 8)/36 + (x - 12)/54 + x/72 = 1

multiplying by 216 (LCD) ___ 6x - 48 + 4x - 48 + 3x = 216 ___ 13x = 312

x = 24