document.write( "Question 645397: A swimming pool can be filled by a pipe in 6 hours and it requires 9 hours to drain it. If the drain was accidentally left open for 6 hours, while the pool was being filled, how long will it take to fill the pool? \n" ); document.write( "

Algebra.Com's Answer #405444 by Edwin McCravy(20055) $\"\"$ $\"About$

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A swimming pool can be filled by a pipe in 6 hours and it requires 9 hours to drain it. If the drain was accidentally left open for 6 hours, while the pool was being filled, how long will it take to fill the pool?
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document.write( "In your head:\r\n" );
document.write( "The LCM of 6 hours and 9 hours is 18 hours.  In 18 hours the fill-pipe will\r\n" );
document.write( "fill the pool 3 times and the drain pipe will have drained it 2 times, so\r\n" );
document.write( "that's 3-2 = 1 pool filled in 18 hours.  Answer: 18 hours.\r\n" );
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document.write( "By algebra.\r\n" );
document.write( "The fill rate of the fill pipe is 1 pool per 6 hours or 1/6 pool per hour.\r\n" );
document.write( "The \"fill\" rate of the drain pipe is the loss of one pool per 9 hours, or the\r\n" );
document.write( "loss of 1/9 pool per hour, and we indicate a negative rate with a negative\r\n" );
document.write( "sign, -1/9 pool per hour. The combined fill rate of both pipes is 1 pool per x\r\n" );
document.write( "hours of 1/x pool per hour.  So the equation is gotten by equating the sum of\r\n" );
document.write( "the fill rates to the combined fill rate: \r\n" );
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document.write( "                  1/6 - 1/9 = 1/x\r\n" );
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document.write( "Multiply that through by 18x and solve to get 18 hours.\r\n" );
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document.write( "Edwin

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