document.write( "Question 323669: A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job? \n" ); document.write( "

Algebra.Com's Answer #231698 by Edwin McCravy(20054) $\"\"$ $\"About$

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A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9 days; if A and C work together, the job will take 8 days. In how many days can each man working alone do the job?
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document.write( "Make this chart:\r\n" );
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document.write( "                   Number of jobs    Time in      Rate in\r\n" );
document.write( "                    finished          days        jobs/day\r\n" );
document.write( "A working alone\r\n" );
document.write( "B working alone\r\n" );
document.write( "C working alone\r\n" );
document.write( "A, B & C together\r\n" );
document.write( "B and C together\r\n" );
document.write( "A and C together\r\n" );
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document.write( "Let A working alone be able to do 1 job in x days.\r\n" );
document.write( "Let B working alone be able to do 1 job in y days.\r\n" );
document.write( "Let C working alone be able to do 1 job in z days. \r\n" );
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document.write( "So fill in x, y, and z for their times alone, and fill in 6, 9,\r\n" );
document.write( "and 8 for the times for the various combinations or workers\r\n" );
document.write( "given:\r\n" );
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document.write( "                   Number of jobs    Time in      Rate in\r\n" );
document.write( "                    finished          days        jobs/day\r\n" );
document.write( "A working alone                        x\r\n" );
document.write( "B working alone                        y\r\n" );
document.write( "C working alone                        z\r\n" );
document.write( "A, B & C together                      6\r\n" );
document.write( "B and C together                       9\r\n" );
document.write( "A and C together                       8\r\n" );
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document.write( "In every case we are talking about doing exactly 1 job, so\r\n" );
document.write( "fill in 1's for the number of jobs in every case:\r\n" );
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document.write( "                   Number of jobs    Time in      Rate in\r\n" );
document.write( "                    finished          days        jobs/day\r\n" );
document.write( "A working alone         1              x\r\n" );
document.write( "B working alone         1              y\r\n" );
document.write( "C working alone         1              z\r\n" );
document.write( "A, B & C together       1              6\r\n" );
document.write( "B and C together        1              9\r\n" );
document.write( "A and C together        1              8\r\n" );
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document.write( "Fill in the rates by dividing the number of jobs by the number\r\n" );
document.write( "of days:\r\n" );
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document.write( "                   Number of jobs    Time in      Rate in\r\n" );
document.write( "                    finished          days        jobs/day\r\n" );
document.write( "A working alone         1              x           \r\n" );
document.write( "B working alone         1              y          \r\n" );
document.write( "C working alone         1              z          \r\n" );
document.write( "A, B & C together       1              6          \r\n" );
document.write( "B and C together        1              9           \r\n" );
document.write( "A and C together        1              8          \r\n" );
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document.write( "Now form three equations from\r\n" );
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document.write( "       A's rate + B's rate + C's rate = A,B, and C's rate together\r\n" );
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document.write( "                  B's rate + C's rate = B and C's rate together\r\n" );
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document.write( "                  A's rate + C's rate = A and C's rate together                  \r\n" );
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document.write( "So we have this system:\r\n" );
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document.write( "Subtract the second equation from the first equation:\r\n" );
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document.write( "So it will take A 18 days to do the job working alone.\r\n" );
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document.write( "Subtract the third equation from the first equation:\r\n" );
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document.write( "So it will take B 24 days to do the job working alone.\r\n" );
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document.write( "To find z, substitute for x and y\r\n" );
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document.write( "Multiply every term by 72z to clear of fractions\r\n" );
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document.write( "So it will take C 14.4 days to finish the job working alone.\r\n" );
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document.write( "Edwin

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