SOLUTION: Three workers have to do a certain job. The first worker can finish the job in 8 hours. The second worker can finish the job in 4 hours. The third worker can also finish the job in

Question 1150748: Three workers have to do a certain job. The first worker can finish the job in 8 hours. The second worker can finish the job in 4 hours. The third worker can also finish the job in 4 hours. How long will it take the three workers to finish the job if they work together?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

In one hour, they can do = of the job working together. Hence, they can complete the entire job in hours = 8*12 minutes = 96 minutes = 1 hour and 36 minutes.

Solved.

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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
    - Joint-work problems for 3 participants

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

Tutor @ikleyn has shown the typical algebraic solution method for this kind of problem.

Here are two alternative methods....

(1) logical reasoning and some simple arithmetic....

The worker who takes 8 hours to do the job alone takes twice as long as each of the others. That means he works half as fast.

So the three of them working together is like 2.5 workers working at the rate that it takes one of them to do the job alone.

So the time it takes 2.5 workers to do the job at that rate is 4/2.5 = 8/5 hours.

(2) using the least common multiple of the given times for the three workers....

The numbers of hours for the three workers each to do the job alone are 8, 4, and 4. The LCM of those numbers is 8.

Consider what the three workers could do in 8 hours:

The first worker could do the job once.
The second worker could do the job 8/4 = 2 times.
The third worker could do the job 8/4 = 2 times.

So the three of them together in 8 hours could do the job 1+2+2=5 times.

So the three of them can do the one job in 8/5 hours.

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