document.write( "Question 464785: it takes Tom and John 2 hours to do a certain job,it takes tom and harry 3 hours to do the same job and it takes john and harry 4 hours to do the same job. how long would it take tom, john and harry to do the job if all 3 worked together? \n" ); document.write( "
Algebra.Com's Answer #318484 by Edwin McCravy(20056)\"\" \"About 
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it takes Tom and John 2 hours to do a certain job,it takes tom and harry 3 hours to do the same job and it takes john and harry 4 hours to do the same job. how long would it take tom, john and harry to do the job if all 3 worked together?
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document.write( "Make the chart below.  The number of jobs done in all cases is 1.\r\n" );
document.write( "Let t = Tom's hours to do the 1 job alone\r\n" );
document.write( "Let j = John's hours to do the 1 job alone\r\n" );
document.write( "Let h = Harry's hours to do the 1 job alone\r\n" );
document.write( "Let x = the answer, the number of hours it would take if\r\n" );
document.write( "all three worked together.\r\n" );
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document.write( "                          number of\r\n" );
document.write( "                          jobs done       time in hrs     rate in jobs/hr \r\n" );
document.write( "Tom only                      1                t               \r\n" );
document.write( "John only                     1                j               \r\n" );
document.write( "Harry only                    1                h                \r\n" );
document.write( "Tom & John                    1                2               \r\n" );
document.write( "Tom & Harry                   1                3               \r\n" );
document.write( "John & Harry                  1                4               \r\n" );
document.write( "Tom, John & Harry             1                x               \r\n" );
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document.write( "Now we fill in all the rates in jobs/hour by dividing the number of\r\n" );
document.write( "jobs by the number of hours:\r\n" );
document.write( "                          number of\r\n" );
document.write( "                          jobs done       time in hrs     rate in jobs/hr \r\n" );
document.write( "Tom only                      1                t               1/t\r\n" );
document.write( "John only                     1                j               1/j\r\n" );
document.write( "Harry only                    1                h               1/h \r\n" );
document.write( "Tom & John                    1                2               1/2\r\n" );
document.write( "Tom & Harry                   1                3               1/3\r\n" );
document.write( "John & Harry                  1                4               1/4\r\n" );
document.write( "Tom, John & Harry             1                x               1/x\r\n" );
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document.write( "Tom's rate + John's rate = Tom & John's rate together \r\n" );
document.write( "1/t + 1/j = 1/2\r\n" );
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document.write( "Tom's rate + Harry's rate = Tom & Harry's rate together\r\n" );
document.write( "1/t + 1/h = 1/3\r\n" );
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document.write( "John's rate + Harry's rate = John & Harry's rate together\r\n" );
document.write( "1/j + 1/h = 1/4\r\n" );
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document.write( "So we have this system of equations:\r\n" );
document.write( "1/t + 1/j = 1/2\r\n" );
document.write( "1/t + 1/h = 1/3\r\n" );
document.write( "1/j + 1/h = 1/4\r\n" );
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document.write( "Let A = 1/t, B = 1/j,  C = 1/h\r\n" );
document.write( "A + B = 1/2\r\n" );
document.write( "A + C = 1/3\r\n" );
document.write( "B + C = 1/4\r\n" );
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document.write( "Clear of fractions:\r\n" );
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document.write( "2A + 2B = 1\r\n" );
document.write( "3A + 3C = 1\r\n" );
document.write( "4B + 4C = 1\r\n" );
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document.write( "Line up like terms:\r\n" );
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document.write( "2A + 2B      = 1\r\n" );
document.write( "3A      + 3C = 1\r\n" );
document.write( "     4B + 4C = 1\r\n" );
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document.write( "Can you can solve that by elimination?  \r\n" );
document.write( "If you don't know how, post again asking \r\n" );
document.write( "how to solve that system by elimination.\r\n" );
document.write( "answers:\r\n" );
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document.write( "A = 7/24, B = 5/24, C = 1/24\r\n" );
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document.write( "A = 1/t = 7/24 jobs/hour is Tom's rate\r\n" );
document.write( "B = 1/j = 5/24 jobs/hour is John's rate\r\n" );
document.write( "C = 1/h = 1/24 jobs/hour is Harry's rate\r\n" );
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document.write( "Now we use the equation:\r\n" );
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document.write( "Tom's rate + John's rate + Harry's rate = Tom, John & Harry's combined rate\r\n" );
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document.write( "                     7/24 + 5/24 + 1/24 = 1/x\r\n" );
document.write( "Multiply through by LCD of 24x\r\n" );
document.write( "                            7x + 5x + x = 24\r\n" );
document.write( "                                    13x = 24                                \r\n" );
document.write( "                                      x = 24/13\r\n" );
document.write( "                                      x = 1 11/13 hours\r\n" );
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document.write( "Edwin

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