document.write( "Question 472710: Jun can finish an accounting work in 8 hours, while Leo can do the same in 6 hours. After 2 hours of working together, Jun left Leo for lunch and Leo finished the job. Find the amount of time for Leo to finish the job. \n" ); document.write( "
Algebra.Com's Answer #324076 by Edwin McCravy(20056) $\"\"$ $\"About$
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Jun can finish an accounting work in 8 hours, while Leo can do the same in 6 hours. After 2 hours of working together, Jun left Leo for lunch and Leo finished the job. Find the amount of time for Leo to finish the job.
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document.write( "Make this chart:\r\n" );
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document.write( "                                          number of     Time\r\n" );
document.write( "                                          jobs or       spent    Rate\r\n" );
document.write( "                                          fraction of    in       in\r\n" );
document.write( "                                          job done      hours   jobs/hr\r\n" );
document.write( "Jun working alone for 8 hrs                   \r\n" );
document.write( "Leo working alone for 6 hrs\r\n" );
document.write( "Jun & Leo working together for 2 hrs\r\n" );
document.write( "Leo working alone finishing the job\r\n" );
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document.write( "Let x be the answer, so put x for the time Leo spent finishing the job.\r\n" );
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document.write( "Jun can do 1 complete job in 8 hours, so put 1 for the number of jobs on\r\n" );
document.write( "the top line and 8 for his time spent.\r\n" );
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document.write( "Leo can do 1 complete job in 6 hours, so put 1 for the number of jobs on\r\n" );
document.write( "the second line and 6 for his time spent.  Put 2 on the third line for \r\n" );
document.write( "the time they spent working together:\r\n" );
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document.write( "                                          number of     Time\r\n" );
document.write( "                                          jobs or       spent    Rate\r\n" );
document.write( "                                          fraction of    in       in\r\n" );
document.write( "                                          job done      hours   jobs/hr\r\n" );
document.write( "Jun working alone for 8 hrs                   1           8\r\n" );
document.write( "Leo working alone for 6 hrs                   1           6\r\n" );
document.write( "Jun & Leo working together for 2 hrs                      2\r\n" );
document.write( "Leo working alone finishing the job                       x\r\n" );
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document.write( "Fill in the rates in jobs/hr for the top two lines by dividing the\r\n" );
document.write( "number of jobs by the number of hours.\r\n" );
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document.write( "                                          number of     Time\r\n" );
document.write( "                                          jobs or       spent    Rate\r\n" );
document.write( "                                          fraction of    in       in\r\n" );
document.write( "                                          job done      hours   jobs/hr\r\n" );
document.write( "Jun working alone for 8 hrs                   1           8       1/8\r\n" );
document.write( "Leo working alone for 6 hrs                   1           6       1/6\r\n" );
document.write( "Jun & Leo working together for 2 hrs                      2\r\n" );
document.write( "Leo working alone finishing the job                       x\r\n" );
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document.write( "Next we can fill in 1/6 also for Leo's rate working alone to finish the job\r\n" );
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document.write( "                                          number of     Time\r\n" );
document.write( "                                          jobs or       spent    Rate\r\n" );
document.write( "                                          fraction of    in       in\r\n" );
document.write( "                                          job done      hours   jobs/hr\r\n" );
document.write( "Jun working alone for 8 hrs                   1           8       1/8\r\n" );
document.write( "Leo working alone for 6 hrs                   1           6       1/6\r\n" );
document.write( "Jun & Leo working together for 2 hrs                      2\r\n" );
document.write( "Leo working alone finishing the job                       x       1/6\r\n" );
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document.write( "To fill in the rate for Jun & Leo working together we add their rates:\r\n" );
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document.write( "                                  +  \r\n" );
document.write( "                                  + \r\n" );
document.write( "                                                   \r\n" );
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document.write( "So we put 7/24 for their combined rate on the third line:\r\n" );
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document.write( "                                          number of     Time\r\n" );
document.write( "                                          jobs or       spent    Rate\r\n" );
document.write( "                                          fraction of    in       in\r\n" );
document.write( "                                          job done      hours   jobs/hr\r\n" );
document.write( "Jun working alone for 8 hrs                   1           8       1/8\r\n" );
document.write( "Leo working alone for 6 hrs                   1           6       1/6\r\n" );
document.write( "Jun & Leo working together for 2 hrs                      2      7/24\r\n" );
document.write( "Leo working alone finishing the job                       x       1/6\r\n" );
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document.write( "Now we can fill in the fractions of the job done on the bottom two lines\r\n" );
document.write( "by multiplying the rates in jobs/hr by the time in hours:\r\n" );
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document.write( "·2 =   and ·x = \r\n" );
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document.write( "                                          number of     Time\r\n" );
document.write( "                                          jobs or       spent    Rate\r\n" );
document.write( "                                          fraction of    in       in\r\n" );
document.write( "                                          job done      hours   jobs/hr\r\n" );
document.write( "Jun working alone for 8 hrs                   1           8       1/8\r\n" );
document.write( "Leo working alone for 6 hrs                   1           6       1/6\r\n" );
document.write( "Jun & Leo working together for 2 hrs       7/12           2      7/24\r\n" );
document.write( "Leo working alone finishing the job         x/6           x       1/6\r\n" );
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document.write( "The equation comes from:\r\n" );
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document.write( "Multiply through by 12:\r\n" );
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document.write( " hours.\r\n" );
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document.write( "Edwin
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