document.write( "Question 694131: Chris and Manny work together for 6 hours to landscape a yard before Chris has to leave the job. Manny finishes the yard alone in 10 hours. If Chris can landscape a yard in 18 hours working alone, how long does it take Manny working alone to do the job? \n" ); document.write( "
Algebra.Com's Answer #427769 by Edwin McCravy(20054)\"\" \"About 
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Chris and Manny work together for 6 hours to landscape a yard before Chris has to leave the job. Manny finishes the yard alone in 10 hours. If Chris can landscape a yard in 18 hours working alone, how long does it take Manny working alone to do the job?
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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\r\n" );
document.write( "                        Fraction      Time in      Rate in   \r\n" );
document.write( "                        Thereof         hours      jobs/hour\r\n" );
document.write( "------------------------------------------------------------               \r\n" );
document.write( "Chris alone (1 job)            \r\n" );
document.write( "Manny alone (1 job)    \r\n" );
document.write( "C&M together (6 hrs)         \r\n" );
document.write( "Manny alone (10 hrs) \r\n" );
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document.write( ">>...how long does it take Manny working alone to do the job?...<<\r\n" );
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document.write( "Let the answer to that it takes Manny x hours to do 1 job. So\r\n" );
document.write( "we fill in 1 for Manny's number of jobs and x hours for the time.\r\n" );
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document.write( ">>...Chris can landscape a yard in 18 hours working alone...<<\r\n" );
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document.write( "So we fill in 1 for Chris' number of jobs and 18 hours for the time.\r\n" );
document.write( "And we fill in 6 and 10 for the other given times:\r\n" );
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document.write( "                        Number of \r\n" );
document.write( "                        Jobs or\r\n" );
document.write( "                        Fraction      Time in      Rate in   \r\n" );
document.write( "                        Thereof         hours      jobs/hour\r\n" );
document.write( "------------------------------------------------------------\r\n" );
document.write( "Chris alone (1 job)        1            18                                      \r\n" );
document.write( "Manny alone (1 job)        1             x\r\n" );
document.write( "C&M together (6 hrs)                     6   \r\n" );
document.write( "Manny alone (10 hrs)                    10\r\n" );
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document.write( "Next we fill the rates in jobs/hour by dividing the number of jobs\r\n" );
document.write( "by the number of hours in the first two lines:\r\n" );
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document.write( "                        Number of \r\n" );
document.write( "                        Jobs or\r\n" );
document.write( "                        Fraction      Time in      Rate in   \r\n" );
document.write( "                        Thereof         hours      jobs/hour\r\n" );
document.write( "------------------------------------------------------------\r\n" );
document.write( "Chris alone (1 job)        1            18           1/18\r\n" );
document.write( "Manny alone (1 job)        1             x           1/x\r\n" );
document.write( "C&M together (6 hrs)                     6   \r\n" );
document.write( "Manny alone (10 hrs)                    10\r\n" );
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document.write( "Since Manny's rate alone for 10 hours is the same as his rate when\r\n" );
document.write( "doing 1 whole job, we can also put 1/x for Manny's rate for the 10 hours\r\n" );
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document.write( "                        Number of \r\n" );
document.write( "                        Jobs or\r\n" );
document.write( "                        Fraction      Time in      Rate in   \r\n" );
document.write( "                        Thereof         hours      jobs/hour\r\n" );
document.write( "------------------------------------------------------------\r\n" );
document.write( "Chris alone (1 job)        1            18           1/18\r\n" );
document.write( "Manny alone (1 job)        1             x           1/x\r\n" );
document.write( "C&M together (6 hrs)                     6   \r\n" );
document.write( "Manny alone (10 hrs)                    10           1/x\r\n" );
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document.write( "Chris and Manny's combined rate is the sum of their rates or 1/18 + 1/x,\r\n" );
document.write( "So we fill in that for their combined rate (C&M together):\r\n" );
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document.write( "                        Number of \r\n" );
document.write( "                        Jobs or\r\n" );
document.write( "                        Fraction      Time in      Rate in   \r\n" );
document.write( "                        Thereof         hours      jobs/hour\r\n" );
document.write( "------------------------------------------------------------\r\n" );
document.write( "Chris alone (1 job)        1            18           1/18 \r\n" );
document.write( "Manny alone (1 job)        1             x           1/x\r\n" );
document.write( "C&M together (6 hrs)                     6       1/18 + 1/x\r\n" );
document.write( "Manny alone (10 hrs)                    10           1/x\r\n" );
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document.write( "Next we get the fraction of a job that C&M did together in 6 hours,\r\n" );
document.write( "by multiplying their combined rate by the time 6 hours.  We get the \r\n" );
document.write( "fraction of a job that Manny did alone in the 10 hours, by multiplying \r\n" );
document.write( "Manny's rate 1/x by the time 10 hours.  \r\n" );
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document.write( "                        Number of \r\n" );
document.write( "                        Jobs or\r\n" );
document.write( "                        Fraction      Time in      Rate in   \r\n" );
document.write( "                        Thereof         hours      jobs/hour\r\n" );
document.write( "------------------------------------------------------------\r\n" );
document.write( "Chris alone (1 job)        1            18           1/18 \r\n" );
document.write( "Manny alone (1 job)        1             x           1/x\r\n" );
document.write( "C&M together (6 hrs)  6(1/18 + 1/x)      6       1/18 + 1/x\r\n" );
document.write( "Manny alone (10 hrs)     10/x           10           1/x\r\n" );
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document.write( "The equation comes from:\r\n" );
document.write( "               \"%28matrix%287%2C1%2C%0D%0AFraction%2Cof%2Ca%2C+job%2Cthey%2Cdid%2Ctogether%29%29\" + \"%28matrix%287%2C1%2C%0D%0AFraction%2Cof%2Ca%2C+job%2CManny%2Cdid%2Calone%29%29\" = \"%28matrix%283%2C1%2C%0D%0A1%2Cwhole%2Cjob%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "               \"6%281%2F18%2B1%2Fx%29\" + \"10%2Fx\" = 1\r\n" );
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document.write( "Solve that and get x = 24 hours.  So Manny takes 24 hours\r\n" );
document.write( "to do one job working alone.\r\n" );
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document.write( "  \r\n" );
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document.write( "Edwin
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