SOLUTION: Bill takes 3 days to paint a house, Rory takes 4 days to paint a house and Lucy takes 5 days to paint a house. How long would it take to paint a house (to the nearest hour) if all

Question 1113377: Bill takes 3 days to paint a house, Rory takes 4 days to paint a house and Lucy takes 5 days to paint a house. How long would it take to paint a house (to the nearest hour) if all three of them worked together?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
This is a rate of work problem. The first thing is to find out how much each person does in a unit of time (we'll use 1 hour as that unit):
Bill: 3 days = 72 hours �> Bill paints (1/72) of a house per hour
Rory: 4 days = 96 hours �> Rory paints (1/96) of a house per hour
Lucy: 5 days = 120 hours �> Lucy paints (1/120) of a house per hour
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Now that we have the rate per unit of time, we can add them:
Together, their rate is (1/72) + (1/96) + (1/120) = (1/24)(47/60) = 47/1440 house per hour
That means it will take them 1440/47 hours, or approx. 30.638 hours
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Ans: Rounded to the nearest hour: hours
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Check (in 30.638 hours all 3 working together should paint one house):
Bill paints 30.638*(1/72) = 0.4255
Rory paints 30.638*(1/96) = 0.3191
Lucy paints 30.638*(1/120) = 0.2553

and 0.4255+0.3191+0.2553 = 0.9999 (ok)

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