SOLUTION: It takes Mike 6 hours to paint a house. It takes Jim 4 hours to paint the same house. How long will it take them to paint the house together?

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Question 264416: It takes Mike 6 hours to paint a house. It takes Jim 4 hours to paint the same house. How long will it take them to paint the house together?

Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Mike does 1/6 house per hour.
Jim does 1/4 house per hour.
Together, 1/6 + 1/4 = 5/12 per hour
--> 12/5 = 2.4 hours together.
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Use the shortcut, product/sum
6*4/(6+4) = 24/10
= 2.4

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
It takes Mike 6 hours to paint a house. It takes Jim 4 hours to paint the same house. How long will it take them to paint the house together?
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Mike rate = 1/6 job/hr
Jim rate = 1/4 job/hr
Together rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/6 + 1/4 = 1/x
Multiply thru by 12x to get:
2x + 3x = 12
5x = 12
x = 2.4 hrs (time it would take to paint the house together
x = 2 hr. + 24 minutes
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Cheers,
Stan H.