Question 896197: You have to copy a 500-page document.
There are two copiers In the office:copier a makes 13 copies in 1 minute and copierb makes 18 copies in 1 minute. Let a be the number of pages you put in copier a. Round your answer to the nearest tenth.
A. Write an equation you can use to find out how long it will take to make a copy.
B. How long will it take you to make the copy if you put 200 pages in copier a. Round your answer to the nearest tenth.
C. Which will be faster, the faster copier, or using both copiers by putting 250 pages in each?
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Uniform Rates, doing a task.
RATES in copies/minute
Copier a__________13
Copier b__________18
Obviously copier b is the faster copier.
RT=J for rate, time, quantity of copies, but this rule is for just any one copier.
Let a = number of copies in copier a
Let b = number of copies in copier b
Look at question (C).
You might look at both copiers operating at the same time for as long as needed for each machine to finish a=b=250.
Copier b will finish first.
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 and  .
These are arranged showing both take at least t minutes, but copier a will need an additional x minutes to finish its allotment of copies.
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For copier b,  , which is 13 minutes 53 seconds.
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For copier a, 
some additional arithmetic,
 minutes, which is 5 minutes 21 seconds.
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This means, with 250 copies made in each machine starting at the same time, copier a gives the total time for all 500 copies, requiring:
 , decimal approximation for 19 minutes 14 seconds.
This discussed question (A), did not include question (B), and did most of question (C).
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! A=13 copier
B=18 copier
209.67741935483870967741935483871 by 13 A
290.32258064516129032258064516129 by 18 B
209
291
250/13=19.23 min by 13 A
250/18=13.89 min by 18 B
500/18=27.78 500 by 18 B alone
but if we give 209 to 13 A and 291 to 18 B then it will take about 16 minutes to finish the whole job
Answers:
A)
x/13= t
x= copies to be made by copier a
y/18=T
y =copies to be made by copier B
B)
200/13=15.4 minutes
C)
250/13=19.23 min by 13 A
250/18=13.89 min by 18 B
500/18=27.78 500 by 18 B alone
So it is faster using both copiers at the same time. total time taken would be 19.23 minutes since they are working at the same time.
but if we give 209 to 13 A and 291 to 18 B then it will take about 16 minutes to finish the whole job
13x+18x=500
31x=500
x= abt 16 minutes
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