SOLUTION: i need your help on this question "it will take an apprentice 15 days longer than a qualified painter to complete a job. however, if there is 3 apprentices and 2 qualified painters

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Question 998050: i need your help on this question "it will take an apprentice 15 days longer than a qualified painter to complete a job. however, if there is 3 apprentices and 2 qualified painters working together the job can be completed in 25/8 days. how long will it take one apprentice to do the job?"
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Qualified painter, one-man rate, 1%2Fx
Apprentice, one-man rate, 1%2F%28x%2B15%29

The next or second sentence uses the idea that if n agents are acting, and r is the rate of one agent, then the rate of n agents acting is n*r.

The 3 apprentices and two qualified painters:
This is the rate of the described group: 3%281%2F%28x%2B15%29%29%2B2%281%2Fx%29

That group does 1 job in the given 25%2F8 days.
%283%2F%28x%2B15%29%2B2%2Fx%29%2825%2F8%29=1;
Solve for x in the rational equation.; and then evaluate x+15.