SOLUTION: Persons A and B, working together, can do a job in 6 2/3 hours. A became ill after working with B for 3 hours, leaving B to finish it alone in 8 1/4 hours. How long would it take e

Question 940725: Persons A and B, working together, can do a job in 6 2/3 hours. A became ill after working with B for 3 hours, leaving B to finish it alone in 8 1/4 hours. How long would it take each working alone to finish the job?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
If A and B can finish the job in 6 2/3 hours,then in 3 hours they should have done 3 hours/6.667 hours=45% done. This means it took B 5 1/4 hours (8 1/4hours-3 hours already spent) to do 55% that remained. This means to do 100% would take B 5 1/4 hrs/.055=9.55 hrs. This means B does 1/9.55=.105 or 10.5% of the job in 1 hour. So in 6 2/3 hours B should do 6 2/3 x 10.5%=69.8% of the job.
That means A does the remaining 30.2% in 6 2/3 hrs or 30.2/6 2/3=4.53% per hour or to do it all would require (6 2/3)/.302= 22.1 hours.
So A alone would require 22.1 hours and B alone would require 9.55 hrs.
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