document.write( "Question 574909: If 5 girls and 2 boys work together they can paint a house in a day. Three girls and 6 boys working together can also paint the house in a day. How long would it take one boy to paint the house by himself? \n" ); document.write( "

Algebra.Com's Answer #369325 by stanbon(75887) $\"\"$ $\"About$

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If 5 girls and 2 boys work together they can paint a house in a day. Three girls and 6 boys working together can also paint the house in a day. How long would it take one boy to paint the house by himself?
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\n" ); document.write( "Let girl rate = g
\n" ); document.write( "Let boy's rate = b
\n" ); document.write( "----
\n" ); document.write( "Equations:
\n" ); document.write( "5g + 2b = 1
\n" ); document.write( "3g + 6b = 1
\n" ); document.write( "-------
\n" ); document.write( "Multiply thru 1st equation by 3
\n" ); document.write( "Multiply thru 2nd equation by 5
\n" ); document.write( "--------------------------
\n" ); document.write( "15g + 6b = 3
\n" ); document.write( "15g + 30b = 5
\n" ); document.write( "----
\n" ); document.write( "Subtract and solve for \"b\":
\n" ); document.write( "24b = 2
\n" ); document.write( "b = 1/12 job/day
\n" ); document.write( "----
\n" ); document.write( "Time for a boy to do the job alone 12 days/job
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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