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Question 159527: I am printing books in my house, and I have two printers available. My older printer can print one book in 3 hours, whereas my newer printer can finish a book in 1 hour and 20 minutes. At the same time, while these books are printing, my nephew will tear up one book every 6 hours. How long does it take to complete 38 books?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes to complete 38 books
Now what we are going to be shooting for is the following:
(Rate at which we complete books)*x hours=38 books
Older printer prints at the rate of 1/3 book per hour
Newer printer prints at the rate of 1/(1 1/3) or 3/4 book per hour
Nephew tears up books at the rate of 1/6 book per hour
With all three working together, they work at the rate of:
1/3 + 3/4 - 1/6 or
4/12 + 9/12 -2/12=11/12 book per hour. So our equation to solve is:
(11/12)x=38 multiply each side by 12
11x=456 divide each side by 11
x=41.45hrs or 41hr 27min
CK
In 41.45 hours, old printer prints(1/3)(41.45)=13.82 books
In 41.45 hours, new printer prints (3/4)(41.45)=31.09 books
In 41.45 hours, nephew tears up (1/6)(41.45)=6.91 books
13.82 + 31.09 -6.91=38
38=38
Hope this helps---ptaylor
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