SOLUTION: Two painters, Joe and Sam, will paint a house working together. Working alone, Joe can paint the house in sixteen hours and Sam can paint it in twelve hours. How long will it take

Question 976812: Two painters, Joe and Sam, will paint a house working together. Working alone, Joe can paint the house in sixteen hours and Sam can paint it in twelve hours. How long will it take Joe and Sam to paint the house working together?
Found 3 solutions by stanbon, richwmiller, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Two painters, Joe and Sam, will paint a house working together. Working alone, Joe can paint the house in sixteen hours and Sam can paint it in twelve hours. How long will it take Joe and Sam to paint the house working together?
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Joe rate:: 1/16 job/hr
Sam rate:: 1/12 job/hr
---
Together rate:: 1/x job/hr
-------
Equation:
rate + rate = together rate
1/16 + 1/12 = 1/x
------
12x + 16x = 12*16
28x = 192
x = 48/7
-----
time to do the job together:: 48/7 hr = 6.86 hrs
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Cheers,
Stan H.
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Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
x/16+x/12=1
12x/192+16x/192=1
28x=192
x=192/28=6.857142857142857 hours= 6 hours 51.42857142857143 minutes
check
6.857142857142857/16+6.857142857142857/12=1
0.4285714285714286+0.5714285714285714=1
1=1

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Two painters, Joe and Sam, will paint a house working together. Working alone, Joe can paint the house in sixteen hours and Sam can paint it in twelve hours. How long will it take Joe and Sam to paint the house working together?

Joe can do of work in 1 hour
Sam can do of work in 1 hour
Let time be T
Then we get:
3T + 4T = 48 ------- Multiplying by LCD, 48T
7T = 48
T, or time = hours
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