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 
<pre><font size = 5 color = "indigo"><b>
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</pre>