Question 1058134
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A gardener completes maintenance in 12 hours. Another gardener takes 10 hours. How long will it take both gardeners?
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<pre>
The rate of the 1-st gardener is {{{1/12}}} job per hour.
It means that he does {{{1/12}}} of his job in hour. In each hour.

The rate of the 2-nd gardener is {{{1/10}}} job per hour.
It means that he does {{{1/10}}} of his job in hour. In each hour.

When they work together, their rates are added.
Together they do {{{1/12 + 1/10}}} of the entire work per hour.

{{{1/12 + 1/10}}} = {{{10/120 + 12/120}}} = {{{22/120}}} of the job per hour.

Hence, they will complete the job in {{{120/22}}} = {{{60/11}}} hours = {{{5}}} {{{5/11}}} hours.
</pre>

<U>The lesson to learn from this solution</U>: 


&nbsp;&nbsp;&nbsp;&nbsp; There is no need to solve equations.
&nbsp;&nbsp;&nbsp;&nbsp; You can solve it using simple logic.
&nbsp;&nbsp;&nbsp;&nbsp; You also are supposed to operate freely with fractions. That's all.


&nbsp;&nbsp;&nbsp;&nbsp; Simple logic and fractions.


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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>".