SOLUTION: Copier A can make 300 photocopies of a page in 15 minutes. Copier B can do the same job in 12 minutes. If both copiers work together, how long will it take them to do the same job?

Question 385919: Copier A can make 300 photocopies of a page in 15 minutes. Copier B can do the same job in 12 minutes. If both copiers work together, how long will it take them to do the same job?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Copier A can make 300 photocopies of a page in 15 minutes. Copier B can do the same job in 12 minutes. If both copiers work together, how long will it take them to do the same job?
Let x = minutes it would take to do the job if both copiers work together.
1/x = work rate when both copiers work together
copy A can do the job in 15 minutes while working alone
copy A work rate =1/15
copy B can do the job in 12 minutes while working alone
copy B work rate =1/12
comparing hourly work rates
1/15+1/12=1/x
LCD=60
4+5=60/x
x=60/9 =6+2/3 minutes
ans: It would take 2 copiers working together 6+2/3 minutes to finish the same job
check:in 6+2/3 minutes, copier A makes( (6+2/3)/15)*300=133+1/3 copies
in 6+2/3 minutes, copier B makes (6+2/3)(12)*300=166+2/3 copies

Note: The problem as given appears more complicated than it is. In setting up the equation to solve the problem, the number of copies to be made are not involved. In my experience, most of these working rate problems like this one can be solved by setting up an equation where the sum of the individual work rates are equal to the work rate when all individual work together.
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