SOLUTION: Machine A can photocopy 1000 pieces of a single file in 5 hours, while Machine B can photocopy 1000 pieces of the same file in 4 hours. How long will it take the two machines, bo

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Machine A can photocopy 1000 pieces of a single file in 5 hours, while Machine B can photocopy 1000 pieces of the same file in 4 hours. How long will it take the two machines, bo      Log On


   

Question 1094523: Machine A can photocopy 1000 pieces of a single file in 5 hours,
while Machine B can photocopy 1000 pieces of the same file in 4
hours. How long will it take the two machines, both working
together to photocopy 1,600 pieces of a file?
please include full solution for future self-study
Thank you!!
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!

1000 pieces in 5 hours --> 200 per hour.
1000 pieces in 4 hours --> 250 per hour.
Together: 450 per hour.
1600 pieces, at 450 per hour --> 1600/450 hours.

1600%2F450+=+160%2F45+=+32%2F9

32/9 hours, or 3 5/9 hours, or 3 hours 33 1/3 minutes.


Or an alternative method of solving the problem....

A takes 5 hours to do 1000 pieces, so it does 1/5 of the job in 1 hour.
B takes 4 hours to do 1000 pieces, so it does 1/4 of the job in 1 hour.
Together in 1 hour, the fraction of the job A and B do in 1 hour is
1%2F5+%2B+1%2F4+=+4%2F20+%2B+5%2F20+=+9%2F20
and so the number of hours it takes them to do the job together is 20/9.

But that job is 1000 pieces; this job is 1600 pieces. So we need to multiply the amount of time by 1600/1000, or 8/5:
%2820%2F9%29%2A%288%2F5%29+=+32%2F9

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
For your self-study,  there is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Rate of work problems
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Using quadratic equations to solve word problems on joint work
    - Solving rate of work problem by reducing to a system of linear equations
    - Selected joint-work word problems from the archive
    - Joint-work problems for 3 participants
    - Had there were more workers, the job would be completed sooner
    - One unusual joint work problem
    - Special joint work problems that admit and require an alternative solution method
    - OVERVIEW of lessons on rate-of-work problems


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.