Question 1163729
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There is a project. Company A needs 24 days to finish. Company B needs 30 days to finish. If A and B collaborate for 8 days, 
then it takes 6 more days for company C to finish the rest. How long does it take for company C alone to finish the project?
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<pre>
Working 8 days, company A will make  {{{8/24}}} = {{{1/3}}}   of the job;  

                company B will make  {{{8/30}}} = {{{4/15}}}  of the job.



So, in 8 days the companies A and B will complete  {{{1/3}}} + {{{4/15}}} = {{{5/15 + 4/15}}} = {{{9/15}}} = {{{3/5}}} of the job.


The rest is  1 - {{{3/5}}} = {{{2/5}}}  of the job;  hence, the rate of company C  is  {{{((2/5))/6}}} = {{{2/30}}} = {{{1/15}}}.


It means that company C can complete the whole project  in 15 days working alone.    <U>ANSWER</U>
</pre>

Solved.


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All you need is to know the notion/conception of the "rate of work" and to have skills manipulating fractions.


You even do not need write and solve equations.


From this point of view, it is a "Pre-algebra" level problem.