document.write( "Question 1005375: 8 womens and 12 girls can paint a large mural in 10 hours. 6 womens and 8 girls can paint the same mural in 14 hours. How long it would take to paint the mural one women? How long it would take to paint the mural one girl?
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Algebra.Com's Answer #621660 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "8 $\"highlight%28women%29\"$ and 12 girls can paint a large mural in 10 hours. 6 $\"highlight%28women%29\"$ and 8 girls can paint the same mural in 14 hours.
\n" ); document.write( "How long it would take to paint the mural one $\"highlight%28woman%29\"$ ? How long it would take to paint the mural one girl?
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document.write( "Let w = number of hours it would take to paint the mural one woman.\r\n" );
document.write( "Let g = number of hours it would take to paint the mural one girl.\r\n" );
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document.write( "Then one woman paints  of the mural per hour. 8 women paint  of the mural per one hour.\r\n" );
document.write( "One girl paints  of the mural per hour. 12 girls paint  of the mural per one hour.\r\n" );
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document.write( "In this way you get the system of two equations \r\n" );
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document.write( " +  = ,   (1)\r\n" );
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document.write( " +  = .    (2)\r\n" );
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document.write( "for two unknowns w and g. To solve it, multiply equation (1) by 2 (both sides) and equation (2) by -3, then add.\r\n" );
document.write( "Thus you exclude the variable g and get an equation for the variable w only:\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "It gives w = 140. Hence, it takes 140 hours for 1 woman to paint the mural.\r\n" );
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document.write( "Now please complete the solution yourself.\r\n" );
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