document.write( "Question 516944: Water can be pumped into or out of a tank via pipes A, B, and C. Pipe A can fill the tank in four hours. Pipe B in six hours. Pipe C can empty the tank in five hours. If the water tank is empty and all three pipes begin opporating at the same time, how long will it take to fill the tank?
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Algebra.Com's Answer #344558 by Edwin McCravy(20055) $\"\"$ $\"About$

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Water can be pumped into or out of a tank via pipes A, B, and C. Pipe A can fill the tank in four hours. Pipe B in six hours. Pipe C can empty the tank in five hours. If the water tank is empty and all three pipes begin opporating at the same time, how long will it take to fill the tank?
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document.write( "Make this chart:\r\n" );
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document.write( "                         Number of          Time required     Rate in   \r\n" );
document.write( "                        tanks filled           in hours      tanks/hour\r\n" );
document.write( "Pipe A alone\r\n" );
document.write( "Pipe B alone\r\n" );
document.write( "Pipe C alone\r\n" );
document.write( "All three together\r\n" );
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document.write( "Let x = the number of hours required for all three to fill one tank,\r\n" );
document.write( "so fill in 1 for the number of tanks filled and x for the number of\r\n" );
document.write( "hours:\r\n" );
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document.write( "                         Number of          Time required     Rate in   \r\n" );
document.write( "                        tanks filled           in hours      tanks/hour\r\n" );
document.write( "Pipe A alone\r\n" );
document.write( "Pipe B alone\r\n" );
document.write( "Pipe C alone\r\n" );
document.write( "All three together           1                    x\r\n" );
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document.write( "Fill in 1 for the number of tanks filled for Pipes A and B.  Fill in\r\n" );
document.write( "-1 for the number of pipes \"filled\" by Pipe C, since emptying one tank\r\n" );
document.write( "is mathematically equivalent to \"filling -1 tank\":\r\n" );
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document.write( "                         Number of          Time required     Rate in   \r\n" );
document.write( "                        tanks filled           in hours      tanks/hour\r\n" );
document.write( "Pipe A alone                 1\r\n" );
document.write( "Pipe B alone                 1\r\n" );
document.write( "Pipe C alone                -1\r\n" );
document.write( "All three together           1                    x\r\n" );
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document.write( "Fill in 4, 6, and 5 hours for time required for A, B, and C \r\n" );
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document.write( "                         Number of          Time required     Rate in   \r\n" );
document.write( "                        tanks filled           in hours      tanks/hour\r\n" );
document.write( "Pipe A alone                 1                    4\r\n" );
document.write( "Pipe B alone                 1                    6\r\n" );
document.write( "Pipe C alone                -1                    5\r\n" );
document.write( "All three together           1                    x\r\n" );
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document.write( "Fill in the four rates in tanks/hour by dividing the number of tanks\r\n" );
document.write( "by the number of hours:\r\n" );
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document.write( "                         Number of          Time required     Rate in   \r\n" );
document.write( "                        tanks filled           in hours      tanks/hour\r\n" );
document.write( "Pipe A alone                 1                    4             1/4\r\n" );
document.write( "Pipe B alone                 1                    6             1/6\r\n" );
document.write( "Pipe C alone                -1                    5            -1/5 \r\n" );
document.write( "All three together           1                    x             1/x\r\n" );
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document.write( "The equation comes from\r\n" );
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document.write( "(Pipe A's rate) + (Pipe B's rate) + (Pipe C's rate) = (All 3's rate)\r\n" );
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document.write( "                     +  +  = \r\n" );
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document.write( "Solve that by first multiplying through by LCD = 60x\r\n" );
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document.write( "Asswer x = 60/13 = 4.615384615 hours = 4 hours 36.9 minutes, \r\n" );
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document.write( "                   \r\n" );
document.write( "Edwin

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