<PRE><B>Question 120361</B>
Two men, A and B, can paint a house in 8 days. A alone can paint it in 12 days. How long will B take to paint the house by himself. 
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Let B = time required by B to paint the house by himself
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Let the completed job = 1
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A simple equation:
{{{8/12}}} + {{{8/B}}} = 1
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Multiply equation by 12B to get rid of the denominators
12B*{{{8/12}}} + 12B*{{{8/B}}} = 12B(1)
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Cancel out the denominators and you have:
8B + 12(8) = 12B
:
8B + 96 = 12B
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96 = 12B - 8B
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96 = 4B
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B = 96/4
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B = 24 days 
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Check solution:
{{{8/12}}} + {{{8/24}}} = 
{{{2/3}}} + {{{1/3}}} = 1; confirms our solution</PRE>