SOLUTION: Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters together to paint the house?

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Question 90003: Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters together to paint the house?
Found 2 solutions by stanbon, tutorcecilia:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters together to paint the house?
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1st painter DATA:
Time = 12 hr/job ; Rate = 1/12 job/hr
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2nd painter DATA:
Time = 8 hr/job ; Rate = 1/8 job/hr
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Together DATA:
Time = x hr/job ; Rate = 1/x job/hr
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EQUATION:
rate + rate = rate together
1/12 + 1/8 = 1/x
Multiply thru by 24x to get:
2x + 3x = 24
x = 24/5 hrs (time for them together to do the job)
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Cheers,
Stan H.

Answer by tutorcecilia(2152) (Show Source):
You can put this solution on YOUR website!

Painter #1 = x/12
Painter #2 = x/8
Total job = 1 job
.
x/12 + x/8 = 1 [simplify]
(24)(x/12 + x/8 = 1) [multiply through by a common denominator to clear the fractions]
.
2x+3x=24 [solve for the x-term]
5x=24
x=24/5
x=4.8 hours
.
Check by plugging (x=4.8) back into the original equation.