document.write( "Question 594695: A carpenter can complete a certain job in 5 hours. After working on the job for 2 hours, an assistant helped finished the job. Together they completed the job in 1 hour. How long might it take the assistant, working alone, to complete a job similar to this one? \n" ); document.write( "

Algebra.Com's Answer #376859 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "Here is a slightly different approach, though essentially it is the same as\r\n" );
document.write( "that of the other tutor.\r\n" );
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\n" ); document.write( "A carpenter can complete a certain job in 5 hours. After working on the job for 2 hours, an assistant helped finish the job. Together they completed the job in 1 hour. How long might it take the assistant, working alone, to complete a job similar to this one?
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document.write( "Make this chart:\r\n" );
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document.write( "                                  Number of    \r\n" );
document.write( "                                  jobs or        Time in      Rate\r\n" );
document.write( "                                  fraction        hours        in \r\n" );
document.write( "                                of job done       worked    jobs/hour\r\n" );
document.write( "Carpenter alone for 1 job\r\n" );
document.write( "Carpenter alone for 2 hours\r\n" );
document.write( "Carpenter and assistant for 1 hour\r\n" );
document.write( "Assistant alone for 1 job\r\n" );
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document.write( "Let x equal the number of hours it would take the assistant to do\r\n" );
document.write( "1 complete job.  So we fill in 1 for the number of jobs and x for\r\n" );
document.write( "the number of hours:\r\n" );
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document.write( "                                    Number of    \r\n" );
document.write( "                                    jobs or        Time in      Rate\r\n" );
document.write( "                                    fraction        hours        in \r\n" );
document.write( "                                  of job done       worked    jobs/hour\r\n" );
document.write( "Carpenter alone for 1 job\r\n" );
document.write( "Carpenter alone for 2 hours\r\n" );
document.write( "Carpenter and assistant for 1 hour\r\n" );
document.write( "Assistant alone for 1 job              1              x\r\n" );
document.write( "

\n" ); document.write( ">>...A carpenter can complete a certain job in 5 hours...<<
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document.write( "So we fill in 1 job and 5 hours on the first line:\r\n" );
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document.write( "                                    Number of    \r\n" );
document.write( "                                    jobs or        Time in      Rate\r\n" );
document.write( "                                    fraction        hours        in \r\n" );
document.write( "                                 of job done       worked    jobs/hour\r\n" );
document.write( "Carpenter alone for 1 job              1              5\r\n" );
document.write( "Carpenter alone for 2 hours\r\n" );
document.write( "Carpenter and assistant for 1 hour\r\n" );
document.write( "Assistant alone for 1 job              1              x\r\n" );
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document.write( "Next we form the rates in jobs/hour by dividing the number of jobs by the\r\n" );
document.write( "number of hours:\r\n" );
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document.write( "                                    Number of    \r\n" );
document.write( "                                    jobs or        Time in      Rate\r\n" );
document.write( "                                    fraction        hours        in \r\n" );
document.write( "                                  of job done      worked    jobs/hour\r\n" );
document.write( "Carpenter alone for 1 job              1              5          1/5\r\n" );
document.write( "Carpenter alone for 2 hours\r\n" );
document.write( "Carpenter and assistant for 1 hour\r\n" );
document.write( "Assistant alone for 1 job              1              x          1/x\r\n" );
document.write( "

\n" ); document.write( ">>...(The carpenter) After working on the job for 2 hours,...<<
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document.write( "Fill in the carpenter's rate as 1/5 and his time this time as 2 hours.\r\n" );
document.write( "\r\n" );
document.write( "                                    jobs or        Time in      Rate\r\n" );
document.write( "                                    fraction        hours        in \r\n" );
document.write( "                                   of job done          worked    jobs/hour\r\n" );
document.write( "Carpenter alone for 1 job              1              5          1/5\r\n" );
document.write( "Carpenter alone for 2 hours                           2          1/5\r\n" );
document.write( "Carpenter and assistant for 1 hour\r\n" );
document.write( "Assistant alone for 1 job              1              x          1/x\r\n" );
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document.write( "Next we use the fact that their rate together is the sum of their rates\r\n" );
document.write( "(like in those math problems about a boat in a stream where you add\r\n" );
document.write( "the rate of the stream to the rate of the boat). So we determine their\r\n" );
document.write( "rate together by adding 1/5 and 1/x, and fill in 1 for the number of hours \r\n" );
document.write( "\r\n" );
document.write( "                                    Number of    \r\n" );
document.write( "                                    jobs or        Time in      Rate\r\n" );
document.write( "                                    fraction        hours        in \r\n" );
document.write( "                                 of job done       worked    jobs/hour\r\n" );
document.write( "Carpenter alone for 1 job              1              5          1/5\r\n" );
document.write( "Carpenter alone for 2 hours                           2          1/5\r\n" );
document.write( "Carpenter and assistant for 1 hour                    1        1/5+1/x\r\n" );
document.write( "Assistant alone for 1 job              1              x          1/x\r\n" );
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document.write( "Now we get the fractions of a job for the middle two lines by multiplying\r\n" );
document.write( "the rate in jobs/hour by hours worked\r\n" );
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document.write( "                                    Number of    \r\n" );
document.write( "                                    jobs or        Time in      Rate\r\n" );
document.write( "                                    fraction        hours        in \r\n" );
document.write( "                                 of job done       worked    jobs/hour\r\n" );
document.write( "Carpenter alone for 1 job              1              5          1/5\r\n" );
document.write( "Carpenter alone for 2 hours           2/5             2          1/5\r\n" );
document.write( "Carpenter and assistant for 1 hour  1(1/5+1/x)        1        1/5+1/x\r\n" );
document.write( "Assistant alone for 1 job              1              x          1/x\r\n" );
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document.write( "The equation comes from:\r\n" );
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document.write( "              \r\n" );
document.write( " +  = \r\n" );
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document.write( "2/5 + (1/5 + 1/x) = 1\r\n" );
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document.write( "Solve that and get 5/2 or 2.5\r\n" );
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document.write( "Edwin

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