Question 1089560
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<pre>
Let x be the time in hours for son to complete the job working alone.
Then the time for the father is x-1 hours.

The son's    rate of work is  {{{1/x}}}      of the job per hour.

The father's rate of work is  {{{1/(x-1)}}}  of the job per hour.

Their combined rate of work is  {{{1/x + 1/(x-1)}}}.

From the other side, the condition says that their combined rate of work is {{{1/8}}}   of the job per hour.


It gives you an equation 

{{{1/x + 1/(x-1)}}} = {{{1/8}}}.


To solve it, multiply both sides by 8x*(x-1). You will get

8(x-1) + 8x = x*(x-1).

Simplify and solve for x:

x^2 - 17x + 8 = 0,

{{{x[1,2]}}} = {{{(17 +- sqrt(17^2 - 4*8))/2}}} = {{{(17 +- sqrt(257))/2}}} = {{{(17 +- 16.03)/2}}}.

Only positive root works: x = {{{(17+16.03)/2}}} = 16.5 hours = 16 hours and 30 minutes (approximately).

<U>Check</U>.  {{{1/16.5 + 1/15.5}}} = 0.1251;   {{{1/8}}} = 0.125.

               Check is good !.

<U>Answer</U>.  It will take approximately 16.5 hours for the son to make this job working alone.
</pre>

Solved.



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>".