document.write( "Question 1013789: need to write an equation and solve\r
\n" ); document.write( "\n" ); document.write( "Nancy takes an hour and a half to rake the lawn, but it takes her only 40 minutes if her sister rakes, too. How long does it take her sister to rake the lawn alone? \n" ); document.write( "

Algebra.Com's Answer #630085 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Nancy takes an hour and a half to rake the lawn, but it takes her only 40 minutes if her sister rakes, too. How long does it take her sister to rake the lawn alone?
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document.write( "Nansy's raking rate is  :  =  of-the-lawn-per-hour.\r\n" );
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document.write( "Let x be raking rate of her sister in the same units of .\r\n" );
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document.write( "Then their joint rate is  of-the-lawn-per-hour.\r\n" );
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document.write( "The equation is \r\n" );
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document.write( " =  = ,   or   ( is 40 minutes of time in hours).\r\n" );
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document.write( "Multiply both sides by 3*(x+2/3). You will get\r\n" );
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document.write( "3 = 2*(x+2/3),   or   3 = 2x + 4/3,   or  2x = 3 -  = .\r\n" );
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document.write( "Hence, x = .\r\n" );
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document.write( "It is the sister's rate. \r\n" );
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document.write( "Therefore, it will take  =  =  hours = 1 hour 12 minutes for the sister to rake the lawn working alone.\r\n" );
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