Question 1046595
.
When Raul and Rudy work together, they can point a car in 8 days. Also, they could point this car if Raul worked 12 days 
and Rudy worked 6 days. How long would it take each of them to point the car alone.
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<pre>
Let "x" be the Raul's rate of work and "y" be Rudy's rate of work
( measured in the unit "car-per-day, {{{car/day}}} ).

Then from the condition you have this system of two linear equations

x + y = {{{1/8}}},      (1)    ( "When Raul and Rudy work together, they can point a car in 8 days." )
12x + 6y = 1.     (2)    ( "they could point this car if Raul worked 12 days 
and Rudy worked 6 days." )

To solve it, express x = {{{1/8 - y}}} from (1) and substitute it into (2). You will get

{{{12/8 - 12y}}} + 6y = 1,  or

3 - 24y + 12y = 2,  or

3 - 12y = 2,  or  3 - 2 = 12y,  or  y = {{{1/12}}}.

Thus you found that the Rudy's rate is {{{1/12}}}.  Hence, he need 12 days to complete the job working alone.

Next, from (1) x = {{{1/8 - 1/12}}} = {{{3/24-2/24}}} = {{{1/24}}}.

It means that Raul's rate is {{{1/24}}}, and Raul needs 24 days to complete the job working alone.

<U>Answer</U>.  Raul needs 24 days to complete the job working alone.
         Rudy needs 12 days to complete the job working alone.
</pre>

There is a bunch of my lessons on joint work problems with detailed solutions

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-problem.lesson>Rate of work problems</A>,

&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>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Solving-rate-of-work-problem-by-reducing-to-a-system-of-linear-equations.lesson>Solving rate of work problem by reducing to a system of linear equations</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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Joint-work-word-problem-for-the-day-of-April-first.lesson>Joint work word problem for the day of April, 1</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Joint-work-word-problems-for-3-4-5-participants.lesson>Joint-work problems for 3 participants</A>.

in this site.


Read them and become an expert in solving this kind of problems.


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>.


which contains many other word problems and many other interesting and useful things.