SOLUTION: Hi! I've been trying this problem for some time and I can't seem to figure it out. A mechanical sorter can process a bag of mail in 18 minutes. After the sorter has been worki

Click here to see ALL problems on Miscellaneous Word Problems

Question 1188240: Hi! I've been trying this problem for some time and I can't seem to figure it out.
A mechanical sorter can process a bag of mail in 18 minutes. After the sorter has been working for some time, it breaks down. The rest of the mail it was sorting is divided equally between two older machines, each of which would take 60 minutes to complete the job working alone. The mail is finished being sorted 20 minutes after the first machine started working. How long did the first machine work before breaking down?
Thank you! :)
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
A mechanical sorter can process a bag of mail in 18 minutes.
After the sorter has been working for some time, it breaks down.
The rest of the mail it was sorting is divided equally between two older machines,
each of which would take 60 minutes to complete the job working alone.
The mail is finished being sorted 20 minutes after the first machine started working.
How long did the first machine work before breaking down?
~~~~~~~~~~~~~~~~

Let "t" be the time under the problem's question, in minutes. First sorter did part of the job before breaking. Two other machines worked 20-t minutes each, and these two machines did parts of the job. The multiplier 2 reflects the fact that TWO machines worked during these 20-t minutes. The "total job" equation is + = 1. Multiply both sides by 180; then simplify and find "t" 10t + 6*(20-t) = 180 10t + 120 - 6t = 180 4t = 180 - 120 = 60 t = = 15 minutes. ANSWER

Solved.

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

It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive
    - Solving rate of work problem by reducing to a system of linear equations
    - Solving joint work problems by reasoning

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.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!
Hi! I've been trying this problem for some time and I can't seem to figure it out.
A mechanical sorter can process a bag of mail in 18 minutes. After the sorter has been working for some time, it breaks down. The rest of the mail it was sorting is divided equally between two older machines, each of which would take 60 minutes to complete the job working alone. The mail is finished being sorted 20 minutes after the first machine started working. How long did the first machine work before breaking down?
Thank you! :)

Let the time that the first machine worked, be T Since the total time taken to do the entire job was 20 minutes, the time the 2 other machines took was "20 - T" minutes At 18 minutes to complete the job, first machine's rate is Fraction of work completed by first machine before breaking down: At 60 minutes to complete the job, each of the other 2 machines' rate is , and both have a rate of Fraction of work completed by other 2 machines after first broke down: With the entire job being completed by the 3 machines in 20 minutes, we get: 5T + 3(20 - T) = 90 ------ Multiplying by LCD, 90 5T + 60 - 3T = 90 5T - 3T = 90 - 60 2T = 30 Time that the first machine worked, or You can do the check!!