document.write( "Question 328840: Tomas can do a job in 4 hours. Julia can do the same job in 6 hours. How many hours will it take the two of them to do the job if they work together?\r
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Algebra.Com's Answer #235594 by Edwin McCravy(20060) $\"\"$ $\"About$

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Tomas can do a job in 4 hours. Julia can do the same job in 6 hours.
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document.write( "Heres the way to do it quickly in your head.  Then we'll do it by algebra,\r\n" );
document.write( "the way your teacher wants you to do it.  But for fun. let's do it the\r\n" );
document.write( "easy way first:\r\n" );
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document.write( "The least common multiple of 4 hours and 6 hours is 12 hours. If they worked\r\n" );
document.write( "together for 12 hours Thomas would do 3 jobs and Julia would do 2 jobs.  So\r\n" );
document.write( "together it would take them 12 hours to do 5 jobs or ths\r\n" );
document.write( "hours to do one job, which is ths or 2.4 hours. \r\n" );
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document.write( "By algebra, make this chart:\r\n" );
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document.write( "             Number of jobs      Time in hours      Rate in jobs/hour\r\n" );
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document.write( "Tomas              \r\n" );
document.write( "Julia              \r\n" );
document.write( "Both together      \r\n" );
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document.write( "Let the time for both together be x. and the times for each are\r\n" );
document.write( "given so fill in all three times:\r\n" );
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document.write( "             Number of jobs      Time in hours      Rate in jobs/hour\r\n" );
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document.write( "Tomas                                 4                 \r\n" );
document.write( "Julia                                 6                 \r\n" );
document.write( "Both together                         x                 \r\n" );
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document.write( "We are interested in how long it take each and both to do just 1 job,\r\n" );
document.write( "so we fill in the number of jobs as 1 in each case:\r\n" );
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document.write( "             Number of jobs      Time in hours      Rate in jobs/hour\r\n" );
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document.write( "Tomas              1                  4                 \r\n" );
document.write( "Julia              1                  6                 \r\n" );
document.write( "Both together      1                  x                 \r\n" );
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document.write( "Next use  to fill in the three\r\n" );
document.write( "rates:\r\n" );
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document.write( "             Number of jobs      Time in hours      Rate in jobs/hour\r\n" );
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document.write( "Tomas              1                  4                 1/4\r\n" );
document.write( "Julia              1                  6                 1/6\r\n" );
document.write( "Both together      1                  x                 1/x\r\n" );
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document.write( "To get the equation, use\r\n" );
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document.write( "     Tomas' rate   +    Julia's rate   =   their rate together\r\n" );
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document.write( "          1/4      +        1/6        =         1/x\r\n" );
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document.write( "Multiply through by LCD 12x\r\n" );
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document.write( "hours.\r\n" );
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document.write( "Edwin

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