SOLUTION: 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

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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      Log On


   



Question 81772: 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?
Found 2 solutions by Edwin McCravy, dolly:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

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?

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%2F7                     7
Press B              1                 1%2Fx                     x
Both presses         1                 1%2F5                     5

Now we use the formula:

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

                          1%2F7 + 1%2Fx = 1%2F5

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: 171%2F2 hours.

Edwin

Answer by dolly(163) About Me  (Show Source):
You can put this solution on YOUR website!
Time taken by press A = 7 hrs.
So work done in 1 hr = 1/7 part
Let the time taken by press B = x hrs
So work done in 1 hr = 1/x part
Together work done in 1 hr = 1/7 + 1/x
= (x + 7)/7x
Given they complete in 5 hrs.
==> they complete 1/5 part in 1 hr
So (x + 7)/7x = 1/5
==> 5(x+7) = 7x
==> 5x + 35 = 7x
==> 35 = 7x - 5x
==> 35 = 2x
==> 35/2 = x
==> 17.5 = x
Thus B takes 17.5 hrs to complete all by itself