# SOLUTION: 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 amo

Algebra ->  Algebra  -> Rate-of-work-word-problems -> SOLUTION: 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 amo      Log On

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 Click here to see ALL problems on Rate-of-work-word-problems 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.Answer by Edwin McCravy(8896)   (Show Source): You can put this solution on YOUR website! 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. Make this chart: number of Time jobs or spent Rate fraction of in in job done hours jobs/hr Jun working alone for 8 hrs Leo working alone for 6 hrs Jun & Leo working together for 2 hrs Leo working alone finishing the job Let x be the answer, so put x for the time Leo spent finishing the job. Jun can do 1 complete job in 8 hours, so put 1 for the number of jobs on the top line and 8 for his time spent. Leo can do 1 complete job in 6 hours, so put 1 for the number of jobs on the second line and 6 for his time spent. Put 2 on the third line for the time they spent working together: number of Time jobs or spent Rate fraction of in in job done hours jobs/hr Jun working alone for 8 hrs 1 8 Leo working alone for 6 hrs 1 6 Jun & Leo working together for 2 hrs 2 Leo working alone finishing the job x Fill in the rates in jobs/hr for the top two lines by dividing the number of jobs by the number of hours. number of Time jobs or spent Rate fraction of in in job done hours jobs/hr Jun working alone for 8 hrs 1 8 1/8 Leo working alone for 6 hrs 1 6 1/6 Jun & Leo working together for 2 hrs 2 Leo working alone finishing the job x Next we can fill in 1/6 also for Leo's rate working alone to finish the job number of Time jobs or spent Rate fraction of in in job done hours jobs/hr Jun working alone for 8 hrs 1 8 1/8 Leo working alone for 6 hrs 1 6 1/6 Jun & Leo working together for 2 hrs 2 Leo working alone finishing the job x 1/6 To fill in the rate for Jun & Leo working together we add their rates: + + So we put 7/24 for their combined rate on the third line: number of Time jobs or spent Rate fraction of in in job done hours jobs/hr Jun working alone for 8 hrs 1 8 1/8 Leo working alone for 6 hrs 1 6 1/6 Jun & Leo working together for 2 hrs 2 7/24 Leo working alone finishing the job x 1/6 Now we can fill in the fractions of the job done on the bottom two lines by multiplying the rates in jobs/hr by the time in hours: ·2 = and ·x = number of Time jobs or spent Rate fraction of in in job done hours jobs/hr Jun working alone for 8 hrs 1 8 1/8 Leo working alone for 6 hrs 1 6 1/6 Jun & Leo working together for 2 hrs 7/12 2 7/24 Leo working alone finishing the job x/6 x 1/6 The equation comes from: Multiply through by 12: hours. Edwin