SOLUTION: One hundred years ago, a master silversmith could make a set of tankards in 8 days less time than his apprentice. However, the smith would charge $25 per day, while the apprentice

Question 1075980: One hundred years ago, a master silversmith could make a set of tankards in 8 days less time than his apprentice. However, the smith would charge $25 per day, while the apprentice would charge only only $2. Working together, the two could complete such a set of tankards in 3 days. Would it could cost less to have the master do the job alone, to have the apprentice do it alone, or to have both work together? State the cost in each case.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
Let n be the amount of time it took the apprentice to finish a set of tankards. Then the master would take n-8 days. So:
1/n + 1/n-8=1/3
Then:
3(n-8)+3n=n�-8n
n�-14n+24=0
(n-12)(n-2)=0
n=12 or 2
Since 2-8=-6, we take 12 days as the time it took the apprentice to finish the task alone. So, figuring out the cost, it would take the master 4 days to finish, at $25/day=$100 total.
The apprentice takes 12 days, at $2/day=$24 total.
Together is 3 days @$27/day, or $81 total. Those are the final costs for the tankards. ☺☺☺☺
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