document.write( "Question 438028: Sally can clean the house in 6 hours her father can clean the house in 4 hours and her younger brother dennis can completely mess up the house in 8 hours if sally and her father clean and Dennis plays how long will it take to clean the house? \n" ); document.write( "
Algebra.Com's Answer #303018 by Edwin McCravy(20054)\"\" \"About 
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Sally can clean the house in 6 hours her father can clean the house in 4 hours and her younger brother dennis can completely mess up the house in 8 hours if sally and her father clean and Dennis plays how long will it take to clean the house
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document.write( "Make this chart:\r\n" );
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document.write( "        no. of  houses cleaned  |  time |  rate in houses/hour   \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "Sally                           |       |\r\n" );
document.write( "Father                          |       |\r\n" );
document.write( "Dennis                          |       | \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "All 3                           |       |\r\n" );
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document.write( "Let x be the time for all three doing their thing, whether cleaning \r\n" );
document.write( "or playing, to get 1 house clean.  So we put x for the time for all 3:\r\n" );
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document.write( "        no. of  houses cleaned  |  time |  rate in houses/hour   \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "Sally                           |       |\r\n" );
document.write( "Father                          |       |\r\n" );
document.write( "Dennis                          |       | \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "All 3                           |   x   |\r\n" );
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document.write( "Now fill in the 3 times: \r\n" );
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document.write( "        no. of  houses cleaned  |  time |  rate in houses/hour   \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "Sally                           |   6   |\r\n" );
document.write( "Father                          |   4   |\r\n" );
document.write( "Dennis                          |   8   | \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "All 3                           |   x   |\r\n" );
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document.write( "Sally can clean 1 house in 6 hours, so we put 1 for the\r\n" );
document.write( "no. of houses Sally can clean.\r\n" );
document.write( "Her father can clean 1 house in 4 hours, so we put 1 for the\r\n" );
document.write( "no. of houses her father can clean.\r\n" );
document.write( "Dennis can mess up 1 house in 8 hours, so we put -1 for the\r\n" );
document.write( "no. of houses Dennis can clean, because to mess up 1 house is\r\n" );
document.write( "mathematically the same as \"cleaning -1 house\"\r\n" );
document.write( "Since all 3 will be cleaning 1 house, put 1 for the no. of\r\n" );
document.write( "houses cleaned by all 3\r\n" );
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document.write( "        no. of  houses cleaned  |  time |  rate in houses/hour   \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "Sally              1            |   6   |\r\n" );
document.write( "Father             1            |   4   |\r\n" );
document.write( "Dennis            -1            |   8   | \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "All 3              1            |   x   |\r\n" );
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document.write( "Fill in the rates in houses/hour by dividing the no. of\r\n" );
document.write( "houses by the number of hours:\r\n" );
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document.write( "        no. of  houses cleaned  |  time |  rate in houses/hour   \r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "Sally              1            |   6   |        1/6\r\n" );
document.write( "Father             1            |   4   |        1/4\r\n" );
document.write( "Dennis            -1            |   8   |       -1/8\r\n" );
document.write( "--------------------------------------------------------------\r\n" );
document.write( "All 3              1            |   x   |        1/x\r\n" );
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document.write( "Now the equation come from\r\n" );
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document.write( "Sally's rate + Father's rate + Dennis' rate = Rate for all 3\r\n" );
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document.write( "                   1/6 + 1/4 - 1/8 = 1/x\r\n" );
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document.write( "Clear of fractions by multiplying through by LCD of 24x\r\n" );
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document.write( "                     4x + 6x - 3x = 24\r\n" );
document.write( "                               7x = 24\r\n" );
document.write( "                                x = 24/7 = 3 3/7 hours\r\n" );
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document.write( "Edwin
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