Question 1142603
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            I will tell you about two ways of solving such problems.


            The first way is to make an equation and then to solve it.


            Here it is.



<pre>
Let  t be the time (in hours) for the second student to complete the job, working alone.


Since the first student can make the entire job, working alone, in 20 hours, he makes  {{{1/20}}}  of the job per hour.


Since the second student can make the entire job, working alone, in t hours, he makes  {{{1/t}}}  of the job per hour.


Working together, the two students make  {{{1/20}}} + {{{1/t}}} of the job per hour.


From the other side, we know from the condition, that working together, the two students make the job in 7.5 hours  --

hence, they make  {{{1/7.5}}}  part of the job per hour.


It gives you an equation


    {{{1/20}}} + {{{1/t}}} = {{{1/7.5}}}.


At this point the setup is completed: the equation is constructed, and your next step is to solve it.


For it, multiply both sides by 60t to rid off the denominators. You will get


    3t + 60 = 8t.


Simplify and solve for t :


    60 = 8t - 3t

    60 = 5t

    t = 60/5 = 12.



Thus the problem is just solved, and you just got the 


<U>ANSWER</U> :   The second student needs 12 hours to complete the job working alone.
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The second way is to solve the problem WITHOUT making an equation.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Manipulating fractions is ENOUGH.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Here it is.



<pre>
Working together, the two students make the job in 7.5 hours.

Hence, in one hour (in each hour) they make  {{{1/7.5}}}  of the entire job.


You also are given that the first student can make the entire job in 20 hours, working alone.

It means that he makes  {{{1/20}}} of the job per hour.


Hence, the second student make the rest  {{{1/7.5}}} - {{{1/20}}} of the job per hour.


    {{{1/7.5}}} - {{{1/20}}} = {{{2/15}}} - {{{1/20}}} = {{{8/60}}} - {{{3/60}}} = {{{(8-3)/60}}} = {{{5/60}}} = {{{1/12}}} of the job per hour.


It means that the second student will complete the entire job in 12 hours, working alone.
</pre>


You got &nbsp;<U>the same answer</U>.


Now you know &nbsp;<U>TWO &nbsp;WAYS</U> &nbsp;to solve the problem.


--------------------


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. &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.