document.write( "Question 576817: If it takes 20 people to complete as task in 12 days. How many people will it take to complete the task in 8 days? \n" ); document.write( "

Algebra.Com's Answer #370007 by Edwin McCravy(20055) $\"\"$ $\"About$

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If it takes 20 people to complete a task in 12 days. How many people will it
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document.write( "We have two quantities, the number of people and the number of days.\r\n" );
document.write( "We first have to decide whether the two quantities are DIRECTLY\r\n" );
document.write( "proportional or INVERSELY proportional:\r\n" );
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document.write( "The fraction on the left will contain one quantity \"before\" and \"after\",\r\n" );
document.write( "and the fraction on the right will contain the other quantity \"before\"\r\n" );
document.write( "and after.\r\n" );
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document.write( "Direct variation:\r\n" );
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document.write( "When one quantity is INcreased the other quantity is also INcreased, and when\r\n" );
document.write( "one quantity is DEcreased to other quantity is also DEcreased.\r\n" );
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document.write( "If that is the case, then we use this\r\n" );
document.write( "proportion:\r\n" );
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document.write( "Inverse variation:\r\n" );
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document.write( "When one quantity is increased the other quantity is decreased, and when one\r\n" );
document.write( "quantity is decreased the other quantity is increased.\r\n" );
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document.write( "If that is the case, then we have INVERSE variation, and so we must INVERT the\r\n" );
document.write( "second ratio above.\r\n" );
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document.write( "We have to decide whether PEOPLE and DAYS are DIRECTLY or\r\n" );
document.write( "INVERSELY proprotional.  So we ask which of these is true:\r\n" );
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document.write( "1. DIRECTLY{  The MORE people we have working, the MORE days it will take and\r\n" );
document.write( "the FEWER people we have working, the FEWER days it will take them.\r\n" );
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document.write( "or\r\n" );
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document.write( "2. INVERSELY: The MORE people we have working, the FEWER days it will take and\r\n" );
document.write( "The FEWER people we have working, the MORE days it will take them.\r\n" );
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document.write( "Obviously 1 is false and 2 is true\r\n" );
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document.write( "So they are NOT directly proportional so this proportion does not work: \r\n" );
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document.write( "Since the quatities people and days are INVERSELY proportional we INVERT \r\n" );
document.write( "the second ratio and we have this instead:\r\n" );
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document.write( "People in 1st situation = 20\r\n" );
document.write( "People in second situation = ????  (Let that be N people)\r\n" );
document.write( "Days in 1st situation = 12\r\n" );
document.write( "Days in second situation = 8\r\n" );
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document.write( " = \r\n" );
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document.write( "8N = 240\r\n" );
document.write( " N = 30\r\n" );
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document.write( "So it will take 30 people to complete the task in 8 days.\r\n" );
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document.write( "Edwin

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