SOLUTION: Two printers are put to work printing 200 copies of a document. One of the printers takes 2.5 minutes to print a copy; the other will print a copy in 1.5 minutes. a. Let x represe

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Two printers are put to work printing 200 copies of a document. One of the printers takes 2.5 minutes to print a copy; the other will print a copy in 1.5 minutes. a. Let x represe      Log On


   

Question 990397: Two printers are put to work printing 200 copies of a document. One of the printers takes 2.5 minutes to print a copy; the other will print a copy in 1.5 minutes.
a. Let x represent the time in mintes that both copiers work to complete the job. Write an exoression for how many copies both printers will print in x amount of minutes.
b. How long will it take both printers working together to complete the job?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
printers       copies   time    rate
printer         1        2.5    1/2.5
printer         1        1.5    1/1.5
both at once    1        x      1/x


All rates are using 1 copy but different time amounts. The x is for time in minutes for 1 copy; and the individual rates are additive to make the combined rate.

1%2F2.5%2B1%2F1.5=1%2Fx

1%2F%285%2F2%29%2B1%2F%283%2F2%29=1%2Fx
2%2F5%2B2%2F3=1%2Fx
Simplest common denominator, 15x.
%282%2F5%2B2%2F3%29%2815x%29=15
6x%2B10x=15
16x=15
highlight%28x=15%2F16%29---------THIS is how many minutes for the two printers together to make 1 copy; *but in practice, nobody uses more than one printer to make just one copy. This is really 16 copies per each 15 minutes.