Question 81772
<pre><font face = "lucida console">
Printing press A can print an order in 7hours. If printing press B is used
along with press A, the job can be completed in 5hr. How long would it take
printing press B to print the job by itself?
<b>
Make the chart below.  It is just like a D=RT chart except that
D stands for "DEEDS" not "DISTANCE".  In other words, D stands
for the number of DEEDS or printing jobs done in each case.

 
               No of jobs     Rate in jobs per hour     Time in hours

Press A only                                                     

Press B                                                           

Both presses                                                    

------------------------

We read:

>>...press A can print an order in 7 hours...<<

So that's 1 job in 7 hours. So we fill in 1 for the number
of jobs which A alone does and 7 for the number of hours.

               No of jobs     Rate in jobs per hour     Time in hours

Press A only         1                                         7

Press B                                                          

Both presses 

-------------

Next we read:

>>...If printing press B is used along with press A, the job can be 
completed in 5hr

That's 1 job in 5 hours for both presses. So we fill in 1 for the number
of jobs which both presses together do and 5 for the number of hours.

                                                  
               No of jobs     Rate in jobs per hour     Time in hours

Press A only         1                                         7

Press B                                                           

Both presses         1                                         5

-----------------------

Now we read the question:
>>...How long would it take printing press B to print the job by itself?...<<

That asks how many hour would it that press B to do 1 job. So we 
let x be the number of hours press B would take to do 1 job.  Se
we efill in 1 nfor the number of jobs and x for the number of hours. 


               No of jobs     Rate in jobs per hour     Time in hours

Press A only         1                                         7

Press B              1                                         x

Both presses         1                                         5

----------------------

Now we fill in the rates by using the equivalent of

                    DISTANCE
            RATE = ----------
                      TIME

which is:

                       NUMBER of JOBS 
            RATE =   ----------------- 
                            TIME


               No of jobs     Rate in jobs per hour     Time in hours

Press A only         1                 {{{1/7}}}                     7
Press B              1                 {{{1/x}}}                     x
Both presses         1                 {{{1/5}}}                     5

Now we use the formula:

   Rate of Press A + Rate of Press B = Rate of Both presses together

                          {{{1/7}}} + {{{1/x}}} = {{{1/5}}}

Can you solve that? You have to multiply through by the
LCD of 35x.  If you can't solve it post again asking how.
Answer: 17{{{1/2}}} hours.

Edwin</pre>