Question 1087909
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<pre>
Let x be the time for James to make the job working alone.

Then that of Chris is (x+5) hours.


James' rate of work is {{{1/x}}} of the job per hour.

Chris' rate of work is {{{1/(x+5)}}} of the job per hour.


Their combined  rate of work is  {{{1/x + 1/(x+5)}}} of the job per hour.

And the condition says that it is {{{1/((10/3))}}} of the job per hour  ( 3 hours and 20 minutes = {{{10/3}}} of an hour).


It gives you an equation

{{{1/x + 1/(x+5)}}} = {{{1/((10/3))}}},   or, which is the same,

{{{1/x + 1/(x+5)}}} = {{{3/10}}}.


To solve it, multiply both sides  by 10*x*(x+5). You will get

10*(x+5) + 10x = 3x*(x+5).


Solve this quadratic equation to get the 
</pre>

<U>Answer</U>.  Time for James is 5 hours; times for Chris is 10 hours.



It is a typical joint work problem.


There is a bunch of similar solved joint-work problems/samples with detailed explanations in this site. 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=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Using-quadr-eqns-to-solve-word-problems-on-joint-work.lesson>Using quadratic equations to solve word problems on joint work</A> (*)

and especially the lesson marked (*) as the most closest to your problem.



Also, 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>" of the section "<U>Word problems</U>".