Question 1068673
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If Ana can work twice as {{{highlight(cross(much))}}} fast as Eddie, and {{{highlight(cross(jhohn))}}} John can finish the job {{{highlight(cross(less_than))}}} in one hour sooner that of Ana. 
And Eddie can do it alone in 3 hours. How long would it take for the three of them working together to finish the entire job. 
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<pre>
The condition says that Eddie can make a job in 3 hours.
Hence, Ana can do it in 1.5 hours.
Hence, John can finis the job in 1.5-1 = 0.5 hour.

Now, their rates of work are {{{1/3}}} of the job per hour (Eddie), {{{1/1.5}}} (Ana) and {{{1/0.5}}} (John).

Hence, their combined rate of work is the sum

{{{1/3 + 1/1.5 + 1/0.5}}} = {{{1/3 + 2/3 + 6/3}}} = {{{(1 + 2 + 6)/3}}} = {{{9/3}}} = 3 jobs per hour.

Hence, they need {{{1/3}}} of an hour, or 20 minutes, to complete the job working together.
</pre>

Solved.


For a wide variety of similar solved joint-work problems with detailed explanations 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> 

in this site.


Read them and get be trained in solving joint-work 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>.


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>".