document.write( "Question 553883: Working together, Pat, Lindsey, and Robin can dig a drainage ditch in 2 hours. Working alone, Robin can do it in 6 hours, while Pat can do it 2 1/4 hours faster than Lindsay. How long will it take Lindsay to dig the ditch by herself? (Round your answer to two decimal places.)\r
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Algebra.Com's Answer #361123 by AnlytcPhil(1806)\"\" \"About 
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Working together, Pat, Lindsey, and Robin can dig a drainage ditch in 2 hours. Working alone, Robin can do it in 6 hours, while Pat can do it 2 1/4 hours faster than Lindsay. How long will it take Lindsay to dig the ditch by herself? (Round your answer to two decimal places.)
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document.write( "Please help me solve this problem. Thank you very much!\r\n" );
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document.write( "Make this chart:\r\n" );
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document.write( "                              Number of                   Digging rate\r\n" );
document.write( "                              ditches        Hours            in\r\n" );
document.write( "                                dug         Required      ditches/hour\r\n" );
document.write( "Pat digging alone\r\n" );
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document.write( "Lindsey digging alone\r\n" );
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document.write( "Robin diggin alone\r\n" );
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document.write( "All three digging together\r\n" );
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document.write( "Let the answer be x, which is the number of hours required for Lindsay\r\n" );
document.write( "to dig ONE ditch, so we put x for Lindsay's hours required and 1 for\r\n" );
document.write( "the number of ditches.\r\n" );
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document.write( "                              Number of                   Digging rate\r\n" );
document.write( "                              ditches        Hours            in\r\n" );
document.write( "                               to dig         Required    ditches/hour\r\n" );
document.write( "Pat digging alone\r\n" );
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document.write( "Lindsey digging alone            1             x\r\n" );
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document.write( "Robin diggin alone\r\n" );
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document.write( "All three digging together\r\n" );
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\n" ); document.write( ">>...Pat can do it \"2%261%2F4\" hours faster than Lindsay...<<
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document.write( "So we put Pat's time as x - \"2%261%2F4\" and 1 ditch to dig. We SUBTRACT\r\n" );
document.write( "because \"faster\" means LESS time.\r\n" );
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document.write( "                              Number of                   Digging rate\r\n" );
document.write( "                              ditches        Hours            in\r\n" );
document.write( "                               to dig         Required    ditches/hour\r\n" );
document.write( "Pat digging alone                1           x-\"2%261%2F4\" \r\n" );
document.write( "Lindsey digging alone            1            x\r\n" );
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document.write( "Robin diggin alone\r\n" );
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document.write( "All three digging together\r\n" );
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document.write( "Similar, since all the other information is about digging ONE ditch,\r\n" );
document.write( "fill in 1 for the number of ditches to dig in the other two cases.  \r\n" );
document.write( "Also fill in the given number of hours required in each case:\r\n" );
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document.write( "                              Number of                   Digging rate\r\n" );
document.write( "                              ditches        Hours            in\r\n" );
document.write( "                               to dig       Required      ditches/hour\r\n" );
document.write( "Pat digging alone                1           x-\"2%261%2F4\" \r\n" );
document.write( "Lindsey digging alone            1            x\r\n" );
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document.write( "Robin diggin alone               1            6\r\n" );
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document.write( "All three digging together       1            2\r\n" );
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document.write( "Next we fill in the digging rates in ditches/hour by dividing the\r\n" );
document.write( "number of ditches by the hours:\r\n" );
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document.write( "                              Number of                   Digging rate\r\n" );
document.write( "                              ditches        Hours            in\r\n" );
document.write( "                               to dig       Required      ditches/hour\r\n" );
document.write( "Pat digging alone                1           x-\"2%261%2F4\"           \"1%2F%28x%2B2%261%2F4%29\" \r\n" );
document.write( "Lindsay digging alone            1            x              \"1%2Fx\"         \r\n" );
document.write( "Robin diggin alone               1            6              \"1%2F6\"\r\n" );
document.write( "All three digging together       1            2              \"1%2F2\" \r\n" );
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document.write( "The equation comes from:\r\n" );
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document.write( "            \"%28matrix%285%2C1%2C%22Pat%27s%22%2C+digging%2C+rate%2C+working%2C+alone%29%29\" + \"%28matrix%285%2C1%2C%22Lindsay%27s%22%2C+digging%2C+rate%2C+working%2C+alone%29%29\" + \"%28matrix%285%2C1%2C%22Robins%27s%22%2C+digging%2C+rate%2C+working%2C+alone%29%29\" =             \r\n" );
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document.write( "              \"1%2F%28x-2%261%2F4%29\" + \"1%2Fx\" + \"1%2F6\" = \"1%2F2\"\r\n" );
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document.write( "              Let's first simplify \"1%2F%28x-2%261%2F4%29\"\r\n" );
document.write( "  \r\n" );
document.write( "           Change the mixed fraction to an improper fraction \"1%2F%28x-2%261%2F4%29\" = \"1%2F%28x-9%2F4%29\".  \r\n" );
document.write( "           Multiply top and bottom by 4:\r\n" );
document.write( "           \"4%2F%284x-9%29\"\r\n" );
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document.write( "So the equation becomes:\r\n" );
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document.write( "              \"4%2F%284x-9%29\" + \"1%2Fx\" + \"1%2F6\" = \"1%2F2\"\r\n" );
document.write( "  \r\n" );
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document.write( "Solve that by clearing of fractions by multiplying through by the \r\n" );
document.write( "LCD of 6x(4x-9) \r\n" );
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document.write( "    You will get 7.329001404 which we round to 7.33 hours\r\n" );
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document.write( "It takes Robin approximately 7.33 hours to dig one ditch.\r\n" );
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document.write( "Edwin
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