Question 1179997: Aaron works two times as fast as Michael. Aaron can finish a job in 1 hour. If Aaron and Michael are working together, how long will it take them to finish the job?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Aaron twice as fast as Michael
If Aaron needs just 1 hour, then Michael needs 2 hours.
 for ONE JOB, both people together;
You may be able to see the necessary one or two steps in your head.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Informally....
Since Aaron works twice as fast as Michael, Michael is like one-half of Aaron.
When they work together, that is like having 1 1/2 Aarons, or 3/2 Aarons.
When there are 3/2 as many workers, the job takes 2/3 as long.
ANSWER: 2/3 of 1 hour
The same thing, with formal algebra....
Aaron can do the whole job in 1 hour --> 1/1 = fraction of job Aaron does in 1 hour
Aaron works twice as fast as Michael --> 1/2 = fraction of job Michael does in 1 hour
1/1 + 1/2 = 2/2 + 1/2 = 3/2 = fraction of job the two together can do in 1 hour
The number of hours required for the two of them to do the job together is 
Answer by ikleyn(52777)  (Show Source):
You can put this solution on YOUR website! .
Aaron can finish the job in 1 hour.
Michael can do it in 2 hours, according to the condition.
Working together, the two are as productive as 3 instances of Michael.
So, 3 instances of Michael can do the job in 2/3 hours.
It is the same as to say that Aaron an Michael complete the job in 2/3 of an hour, working together.
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
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.
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