document.write( "Question 1188017: FOUR MEN AND 8 WOMEN CAN FINISH A PIECE OF WORK JOINTLY IN 5 DAYS WHILE 3 MEN AND 2
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Algebra.Com's Answer #819063 by ikleyn(52810) $\"\"$ $\"About$

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\n" ); document.write( "FOUR MEN AND 8 WOMEN CAN FINISH A PIECE OF WORK JOINTLY IN 5 DAYS WHILE 3 MEN AND 2
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document.write( "Let m be the rate of work of one man and let w be the rate of work of one woman.\r\n" );
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document.write( "Then we have this system of 2 equations in 2 unknowns\r\n" );
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document.write( "    4m + 8w =      (1)\r\n" );
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document.write( "    3m + 2w =     (2)\r\n" );
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document.write( "To run of the denominator, I will multiply eq(1) by 5 (both sides) and will multiply eq(2) by 20.\r\n" );
document.write( "I will get then\r\n" );
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document.write( "    20m + 40w = 1           (3)\r\n" );
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document.write( "    60m + 40w = 2           (4)\r\n" );
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document.write( "Next, I will subtract eq(3) from eq(2).  I will get\r\n" );
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document.write( "    40m = 1,   hence  m = .\r\n" );
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document.write( "Now from eq((3),\r\n" );
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document.write( "     + 40w = 1,\r\n" );
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document.write( "which gives then\r\n" );
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document.write( "    40w = 1 -  = ,   w = .\r\n" );
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document.write( "The problem is just solved: a single man will do the job in 40 days, working alone;\r\n" );
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document.write( "                            a single woman will do it in 80 days.\r\n" );
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