A and b

Jhone

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May 16, 2021
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a and b can complete any task individually in 60 days and 75 days respectively. A and B start working together and a few days later A leaves work. So if it takes 30 days outside to complete the rest of the work to B, how many days a worked ?
 

HallsofIvy

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Jan 27, 2012
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Your indiscriminate use of "A", "B", and "a", "b" makes this a little hard to read! I am going to stick with "A" and "B". Since A would take 60 days to do the job alone, he works at the rate of 1/60 "job per day". Since B would take 75 days to do the job alone, he works at the rate of 1/75 "job per day". Working together they work at the rate of 1/60+ 1/75= 1/(12*5)+ 1/(25*5)= 25/300+ 12/300= 37/300.

Let "x" be the number of days they work together. The accomplish 37x/300 of the job which leaves (300- 37x)/300 still to be done. B, doing that alone, will take ((300- 37x)/300)(75)= (300- 37x)/4= 30.
 
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