document.write( "Question 785140: if 2 men, 4 women and 2 boys can complete 10 hectare land in ten days then 4 men,6 women and 8 boys can complete 16 hectare land in how many days.if ratio of their efficiency men,women and boys is 5:4:2. \n" ); document.write( "

Algebra.Com's Answer #477384 by Edwin McCravy(20060) $\"\"$ $\"About$

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ratio of their efficiency men, women and boys is 5:4:2.
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document.write( "So:\r\n" );
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document.write( "A ratio can be multiplied or divided through by any positive\r\n" );
document.write( "constant.  So we'll divide it through by 2, so that the \r\n" );
document.write( "smallest rate, the boy's, will correspond to 1.\r\n" );
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document.write( "That is  5 : 4 : 2 =  2.5 : 2 : 1.  \r\n" );
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document.write( "Therefore:\r\n" );
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document.write( "Suppose 1 boy's work rate is x hectares/day\r\n" );
document.write( "Then 1 woman's work rate is 2x hectares/day\r\n" );
document.write( "and 1 man's work rate is 2.5x hectares/day\r\n" );
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\n" ); document.write( "2 men, 4 women and 2 boys can complete 10 hectare land in ten days
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document.write( "The combined rate of 2 men, 4 women and 2 boys = 5x+8x+2x = \r\n" );
document.write( "15x hectares/day\r\n" );
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document.write( "2 men's rate is 2(2.5x) hectares/day or 5x hectares/day\r\n" );
document.write( "4 women's rate is 4(2x) hectares per day or 8x hectares/day\r\n" );
document.write( "2 boys' rate is 2(x) hectares per day or 2x hectares per day\r\n" );
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document.write( "So their combined rate is 10 hectares/10 days or 1 hectare per\r\n" );
document.write( " day.\r\n" );
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document.write( "So we set the two equal:\r\n" );
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document.write( "15x = 1\r\n" );
document.write( "  x =  \r\n" );
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document.write( "So 1 boy's rate is x or  hectares/day,\r\n" );
document.write( "1 woman's rate is 2x or  hectares/day,\r\n" );
document.write( "and 1 man's rate is 2.5x or  hectares/day.\r\n" );
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\n" ); document.write( "4 men, 6 women and 8 boys can complete 16 hectare land in how many days
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document.write( "Let t = how many days are required\r\n" );
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document.write( "Then in t days, \r\n" );
document.write( "4 men can complete 4·t or  hectares\r\n" );
document.write( "6 women can complete 6·t or  hectares\r\n" );
document.write( "8 boys can complete 8·t or  hectares.\r\n" );
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document.write( "So the sum of the hectares they have completed in t days must = 16 hectares\r\n" );
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document.write( "2t = 16\r\n" );
document.write( " t = 8\r\n" );
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document.write( "Answer: 8 days.\r\n" );
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document.write( "Edwin

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