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Question 1022956: A and B do a work respectively in 12 and 15 hours. If they work one by one for one hour each how much time will they take to finish the work?
Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website! The rate for A is 1/12 of a project per hour
The rate for B is 1/15 of a project per hour
So if the two work on the project alternating each hour,
the average rate will be (1/12 + 1/15)/2 of a project per hour
or (9/120) per hour
(9/120)X = 1 project
so X = (120/9) = 13 1/3 approximately
More exactly,
Beginning with A and alternating hourly the amount of work completed will be
1/12 + 1/15 + 1/12 + 1/15 + 1/12 + 1/15 + 1/12 + 1/15 + 1/12 + 1/15 +1/12 + 1/15 + 1/12 = 59/60 of a project for 13 hours
The final 1/60 th of the project will be completed at a rate of 1/15 project per hour. (1/15)X = 1/60
Multiply each side by 15 , X =15/60 or 1/4
So the total time is 13 1/4 hours
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