SOLUTION: There are two machines that produce aluminum cans. The newer machine can produce 7200 cans in 180 minutes. It takes the older machine 360 minutes to produce that many cans. If t

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Question 1146094: There are two machines that produce aluminum cans. The newer machine can produce 7200 cans in 180 minutes. It takes the older machine 360 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 7200 cans?
Found 3 solutions by VFBundy, ikleyn, greenestamps:
Answer by VFBundy(438)   (Show Source):
You can put this solution on YOUR website!
In all the examples, 7200 cans are produced. So, from this point forward, think of producing 7200 cans as the completed job. (Meaning, in your calculations, you will not have to concern yourself with the number 7200 again.)

New machine's rate of work = 1/180 job per minute
Older machine's rate of work = 1/360 job per minute

Rate of work of both machines working together = 1/180 + 1/360 = 2/360 + 1/360 = 3/360 = 1/120 job per minute

Since both machines working together do 1/120 job per minute, it stands to reason that it takes 120 minutes to complete the job.

Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.

1-st machine makes = 40 cans per minute. 2-nd machine makes = 20 cans per minute. Working together, the two machines make 40 + 20 = 60 cans per minute. Working together, they produce 7200 cans in = 120 minutes. ANSWER

It is how such simple joint work problems should be solved.

The quickest way . . .

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

On joint work problems, 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
    - Solving joint work problems by reasoning
    - 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.

The closest to your problem is the lesson marked (*) in the list.

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.

Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!

Both of the responses from other tutors show variations of the standard process for solving "working together" problems like this.

Here is a solution by an alternative method that many students find easier.

(1) The times needed for the two machines to produce 7200 cans are 180 minutes and 360 minutes.
(2) The least common multiple of 180 and 360 is 360; consider what the two machines can do in 360 minutes.
(3) In 360 minutes, the newer machine can produce 2*7200 = 14400 cans; in that same time the older machine can produce 7200 cans. So in 360 minutes the two machines can produce 14400+7200 = 21600 cans.
(4) Since 21600 = 3*7200, the time required for the two machines together to produce 7200 cans is 360/3 = 120 minutes.