SOLUTION: Painter "A" takes 4 hours to paint the house. Painter "B" takes 6 hours to paint the house. How many hours does it take if both painters ("A" & "B") paint the house together?

Question 168633: Painter "A" takes 4 hours to paint the house.
Painter "B" takes 6 hours to paint the house.
How many hours does it take if both painters ("A" & "B") paint the house together?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Painter "A" takes 4 hours to paint the house.
Painter "B" takes 6 hours to paint the house.
How many hours does it take if both painters ("A" & "B") paint the house together?
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You have to find the inverses, how many houses they can paint per hour, then add those up.
Adding up the hours per house doesn't work, because it's an inverse relationship, the more workers you have, the less time it takes.
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For A, it's 1/4 house per hour.
For B, it's 1/6 house per hour.
Together, it's 1/4 + 1/6 = 5/12 houses per hour.
Invert that, and they take 12/5 hours per house, = 2.4 hours.
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When only 2 are involved, a quick way is the product over the sum:
4*6/(4+6) = 24/10 = 2.4 hours.

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