document.write( "Question 726648: 6 people worked for 9 days to complete two fifths of a project. If three joined the original 6 people, how many days were needed to complete the project? \n" ); document.write( "

Algebra.Com's Answer #445243 by Edwin McCravy(20077) $\"\"$ $\"About$

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6 people worked for 9 days to complete two fifths of a project. If three
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document.write( "You can do it in your head.  I'll show you that way and then I'll show you\r\n" );
document.write( "how to do it by algebra:\r\n" );
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document.write( "IN YOUR HEAD.\r\n" );
document.write( "When the 3 joined them, there were one and a half times as many people,\r\n" );
document.write( "but the remaining ths of the job is one and a half times the ths they had\r\n" );
document.write( "already completed, so it would take them the same time, or 9 days.\r\n" );
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document.write( "BY ALGEBRA:\r\n" );
document.write( "Let x = the number of days needed to complete the remaining  of the project.\r\n" );
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document.write( "The 6 people's combined rate is ths of project per 9 days or  or \r\n" );
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document.write( " or  or \r\n" );
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document.write( "Since 3 people is half of 6 people, the three who joined them's combined rate\r\n" );
document.write( "is half that or , since half as many people work at only half the rate \r\n" );
document.write( "of 6 people.\r\n" );
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document.write( "Therefore the combined rate of all 9 people is  or  or \r\n" );
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document.write( "After the three joined them after ths of the project was completed, there was \r\n" );
document.write( "only ths of the project left to do, so we set up this proportion:\r\n" );
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document.write( "1 project is to 15 days as ths of a project is to x days.\r\n" );
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document.write( "          \r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "          x = ·15\r\n" );
document.write( "          x = 9\r\n" );
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document.write( "So 9 more days were needed to complete the project.\r\n" );
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document.write( "Edwin

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