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Question 62751: Another one I'm stuck on help! A long document prints at a rate of 3 pages per minute. Twenty minutes later the same document is being printed out on a printer that prints at a rate of 5 pages per minute. How long will it take the second printer to catch up to the first printer.
Thanks
Found 2 solutions by jai_kos, Edwin McCravy:
Answer by jai_kos(139)   (Show Source):
You can put this solution on YOUR website! Given the speed of the first printer = 3pages perminute
And the speed of the second printer = 5 pages permintue
We shall use the formula for the speed,
Speed of the first printer = number of pages printed / time taken
=> 3 = number of pages printed / 20 + t
3 * (20 +t) = number of pages printed -->(1)
Speed of the second printer = number of pages printed / time taken
=> 5 = number of pages printed / t
5 * t = number of pages printed -->(2)
Equating equation(1) and (2), we get
3(20 + t) = 5 * t
60 + 3t = 5t
60 = 5t - 3t
60 = 2t
60/2 = t
30 = t
Therefore it will take 30min for the second printer to catch up to the first printer.
Answer by Edwin McCravy(20064)  (Show Source):
You can put this solution on YOUR website! Another one I'm stuck on help! A long document prints at a rate of 3 pages per minute. Twenty minutes later the same document is being printed out on a printer that prints at a rate of 5 pages per minute. How long will it take the second printer to catch up to the first printer.
Thanks
This is a DRT problem where D stands
for Documents printed instead of Distance.
Make this chart:
D R T
Slower printer 3(x+20) 3 x+20
Faster printer 5x 5 x
D R T
Slower printer
Faster printer
Fill in the rates as 3 pages per minute and
5 pages per minute, respectively
D R T
Slower printer 3
Faster printer 5
Let x be the number of minutes it takes the
second printer (the faster one) to catch up
to the the 1st (the slower one). Fill that
in.
D R T
Slower printer 3
Faster printer 5 x
Now since the slower printer has already
been printing for 20 minutes before ths
second one starts, its time is 20 minutes
more than the second one. So fill in
x+20 for its time:
D R T
Slower printer 3 x+20
Faster printer 5 x
Now use D = RT to fill in the D's
(numbers of documents printed)
D R T
Slower printer 3(x+20) 3 x+20
Faster printer 5x 5 x
Now we are ready to make the equation.
When the faster printer has caught up,
the numbers of documents printed will
be equal, so we set the two expressions
for D equal:
3(x + 20) = 5x
Solve that and get x = 30 minutes
Checking: Since the faster printer has
been printing for 30 minutes at 5 pages
per minute, it has printed 5×30 or 150
pages. The slower printer has been
printing 20 minutes longer or 50 minutes,
so it has printed 3×50 or 150 pages, also.
Edwin
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