document.write( "Question 881575: 3 men and 6 women finish a job in 9 days while 2 men and 8 women finish it in 12 days.in hie many days will 12 women working alone will finish the same job \n" ); document.write( "
Algebra.Com's Answer #532311 by josgarithmetic(39617)\"\" \"About 
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y = man rate
\n" ); document.write( "x = woman rate\r
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\n" ); document.write( "\n" ); document.write( "\"3y%2A9%2B6x%2A9=1\", the first combination described
\n" ); document.write( "\"27y%2B54x=1\"\r
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\n" ); document.write( "\n" ); document.write( "\"2y%2A12%2B8x%2A12=1\", the second combination described
\n" ); document.write( "\"24y%2B96x=1\"\r
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\n" ); document.write( "\n" ); document.write( "First combination,
\n" ); document.write( "\"27y=1-54x\"
\n" ); document.write( "\"y=%281-54x%29%2F27\"
\n" ); document.write( "substitute into second combination,
\n" ); document.write( "\"24%281-54x%29%2F27%2B96x=1\"
\n" ); document.write( "\"24%281-54x%29%2B96%2A27x=27\"
\n" ); document.write( "\"24-27%2A54x%2B27%2A96x=27\"
\n" ); document.write( "\"27%2A96x-27%2A54x=3\"
\n" ); document.write( "\"27%2896x-54x%29=3\"
\n" ); document.write( "\"42x=3%2F27\"
\n" ); document.write( "\"x=%281%2F9%2A42%29\"
\n" ); document.write( "\"highlight%28x=1%2F378%29\", meaning one woman does 1 job in 378 days working alone.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Man rate: \"y=%281-54x%29%2F27\"
\n" ); document.write( "\"y=%281-54%2F378%29%2F27\"
\n" ); document.write( "\"y=%281-%289%2A3%2A2%29%2F%289%2A2%2A3%2A7%29%29%2F27\"
\n" ); document.write( "\"y=%281-1%2F7%29%2F27=%287%2F7-1%2F7%29%2F27\"
\n" ); document.write( "\"y=6%2F%287%2A27%29\"
\n" ); document.write( "\"highlight%28y=2%2F63%29\", the one man rate, two jobs in 63 days working alone.\r
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\n" ); document.write( "\n" ); document.write( "To answer the question, the expression for 12 women doing the one job will be
\n" ); document.write( "Let t = time in days;
\n" ); document.write( "\"highlight%28highlight%2812%281%2F378%29%2At=1%29%29\"
\n" ); document.write( "Solve for t.
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