Question 488292
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Please help me solve this word problem, I do not understand what to do.
It takes John 30 minutes to clean his house, When his wife helps him, 
it only takes him 18 minutes. How long would it take his wife by herself?
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        Many beginner students don't know what to do when seeing problems like this one.


        Meanwhile, these problems are simple 
        and allow simple solution, which fits good for beginners.



<pre>
Working together, John and his wife make {{{1/18}}}  of the job per minute.

        It is their combined rate of work.


Working alone, John makes  {{{1/30}}}  of the job per minute.

        It is John's individual rate of work.


From this, it is clear that the wife's rate of work is the difference

        {{{1/18}}} - {{{1/30}}} = {{{30/(18*30)}}} - {{{18/(18*30)}}} = {{{(30-18)/(30*18)}}} = {{{12/(30*18)}}} = {{{2/(30*3)}}} = {{{2/90}}} = {{{1/45}}}.


So, the wife's rate of work is  {{{1/45}}}  of the job per minute.


Hence, it requires 45 minutes for the wife to complete the job working alone.    <U>ANSWER</U>
</pre>

Solved.


Simple ?  &nbsp;&nbsp;If you understand it, &nbsp;you will be able to solve thousands other similar problems.



Compare &nbsp;8 &nbsp;lines explanations in my post against &nbsp;50 &nbsp;lines in the post by @Theo.