SOLUTION: A,B, C can do w piece of work in 12 ,15,20 days .If A leaves 2 days after starting the work and C leaves 2 days before its completion ,in how many days the whole work is completed.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A,B, C can do w piece of work in 12 ,15,20 days .If A leaves 2 days after starting the work and C leaves 2 days before its completion ,in how many days the whole work is completed.      Log On


   

Question 1062417: A,B, C can do w piece of work in 12 ,15,20 days .If A leaves 2 days after starting the work and C leaves 2 days before its completion ,in how many days the whole work is completed.
Answer by stanbon(75887) About Me  (Show Source):
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A,B, C can do w piece of work in 12 ,15,20 days .If A leaves 2 days after starting the work and C leaves 2 days before its completion ,in how many days the whole work is completed.
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Note:: Their respective rates are 1/12 jobs/day ; 1/15 jobs/day ; 1/20 jobs/day.
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Assume the whole job takes "x" days
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Equations:
work done + work done + work done = 1 job
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2*(1/12) + (1/15)x + (x-2)(1/20) = 1 job
Multiply thru by 12*15*20 to get:
2*15*20 + 12*20x + 12*15x - 2*12*15 = 12*15*20
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600 + 240x + 180x - 360 = 3600
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420x + 240 = 3600
42x + 24 = 360
42x = 336
x = 8 days (time to do the job)
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Cheers,
Stan H.
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