SOLUTION: Adam Danny and Fred wanted to mow their parents lawn. Adam, working alone, would need twelve hours. Danny could do it in six hours, but Fred would only need four hours. How long w

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Question 1148098: Adam Danny and Fred wanted to mow their parents lawn. Adam, working alone, would need twelve hours. Danny could do it in six hours, but Fred would only need four hours.
How long would it take to finish the job if the three brothers joined forces, working together?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52748)   (Show Source): You can put this solution on YOUR website!
.

Adam makes    of the job per hour.


Danny makes    of the job per hour.


Fred makes    of the job per hour.


Wirking together, the three make   =  =  =   of the job per hour.


Hence, they will complete the job in 2 hours working together.

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
    - 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(13195)   (Show Source): You can put this solution on YOUR website!


As an alternative to the standard algebraic solution shown by the other tutor, using the fractions of the job each worker does in one hour, try this....

The least common multiple (LCM) of the times for the three workers is 12 hours.

Consider how many lawns each of the workers could mow in 12 hours:
Adam could mow 12/12 = 1 of the lawns
Danny could mow 12/6 = 2 of the lawns
Fred could mow 12/4 = 3 of the lawns

So in 12 hours the three workers could mow the lawn 6 times.

That means the time it would take them to mow the one lawn is 12/6 = 2 hours.
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