Question 1095920
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<pre>
In 8 days that two teams worked together, they completed {{{2/3}}} of the job (since the entire job was scheduled for 12 days).


Thus only {{{1/3}}} of the job was remained, and it was done by the second team in 7 days.


Hence, it would take 3*7 = 21 days for the second team to renovate if the first team  does not participate.


Thus the combined rate of work of the two teams is {{{1/12}}} of the job per day,
while the rate of work of the second team is {{{1/21}}} per day.


It implies that the rate of work of the first team is the difference {{{1/12-1/21}}} = {{{21/(12*21) - 12/(12*21)}}} = {{{9/(12*21)}}} = {{{1/(4*7)}}} = {{{1/28}}}.


Hence, it would take 28 days for the first team to renovate if the second team  does not participate.
</pre>

<U>Answer</U>.  28 days for the first team and 21 days for the second team.



<U>Lesson to learn from this solution</U>.


<pre>
    You do not need solve any equations to get the answer.

    What you really need  is  a) to know what the rate of work is;
                              b) to read the condition attentively, and
                              c) to think 1 - 2 minutes before to start writing.
</pre>


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It is a typical joint work problem.


There is a wide variety of similar solved joint-work problems with detailed explanations in this site. &nbsp;See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using Fractions to solve word problems on joint work</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Solving-more-complicated-word-problems-on-joint-work.lesson>Solving more complicated word problems on joint work</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Selected-problems-from-the-archive-on-joint-work-word-problems.lesson>Selected joint-work word problems from the archive</A> 



Read them and get be trained in solving joint-work problems.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic 
"<U>Rate of work and joint work problems</U>" &nbsp;of the section &nbsp;"<U>Word problems</U>".



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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And the last notice:


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;writing by @josgarithmetic is not adequate for this problem.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;for your safety, &nbsp;it is better to ignore it.



Actually, &nbsp;this problem is for &nbsp;5-6 &nbsp;grade students, &nbsp;who didn't learn system of equations yet.