document.write( "Question 823811: Pipe A can fill a tank in 6 hours, and pipe B can fill it in 2 hours less time than it takes drainpipe C to empty the tank. With all three pipes open, it takes 3 hours and 20 minutes to fill the tank. How long does it take drainpipe C to empty the full tank with pipes A and B closed. \n" ); document.write( "

Algebra.Com's Answer #495835 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "This is the correct complete solution:\r\n" );
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\n" ); document.write( "Pipe A can fill a tank in 6 hours,

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document.write( "So Pipe A's tank filling rate is 1 tank per 6 hr or  or

\n" ); document.write( "pipe B can fill it in 2 hours less time than it takes drainpipe C to empty the tank (with pipes A and B closed).

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document.write( "Suppose drainpipe C can drain 1 tank in x hours.  Then drainpipe C's \"filling\"\r\n" );
document.write( "rate is a negative quantity -1 tank per x hours or  or \r\n" );
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pipe B can fill it in 2 hours less time than it takes drainpipe C to empty the tank.

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document.write( "So Pipe B's tank filling rate is 1 tank per x-2 hr or  or \r\n" );
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With all three pipes open, it takes 3 hours and 20 minutes to fill the tank.

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document.write( "3 hours and 20 minutes is  or  hours.  \r\n" );
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document.write( "So A, B, and C's combined filling rate is 1 tank per  hr or  or  or \r\n" );
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document.write( "So we have this equation:\r\n" );
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document.write( "   \r\n" );
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document.write( "   \r\n" );
document.write( "Multiply through by LCD = 30x(x-2)\r\n" );
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document.write( "   5x(x-2) + 30x - 30(x-2) = 3·3x(x-2)\r\n" );
document.write( "5x² - 10x + 30x - 30x + 60 = 9x(x-2)\r\n" );
document.write( "            5x² - 10x + 60 = 9x² - 18x\r\n" );
document.write( "                         0 = 4x² - 8x - 60\r\n" );
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document.write( "Divide through by 4      0 = x² - 2x - 15\r\n" );
document.write( "                         0 = (x - 5)(x + 3)\r\n" );
document.write( "                             x-5=0;   x+3=0\r\n" );
document.write( "                               x=5;     x=-3 (ignore)\r\n" );
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document.write( "Aswer: 5 hours\r\n" );
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document.write( "Edwin

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