Question 1145369
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>1. &nbsp;ALGEBRA &nbsp;solution</U>



<pre>
Let x be the rate of work  of the first tank, in "job per minute", which is "the tank volume per minute".


Then the rate of work of the second tank is  {{{x/6}}}  "the tank volume per minute".


In one minute, two pumps fill  {{{1/216}}}  of the tank volume.


It means that


    x + {{{x/6}}} = {{{1/216}}}.


Multiply both sides of this equation by 216.  You will get


    216x + 36x = 1,

    252x = 1

    x    = {{{1/252}}}.


Hence, the first pump will fill the tank in 252 minutes, working alone.    <U>ANSWER</U>
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>2.  &nbsp;Mental solution &nbsp;(logical reasoning)</U>



<pre>
The first, faster pump works as productively, as 6 slower pumps.


So, the given info, if reformulated, says that 6+1 = 7 slower pumps will fill the tank in 216 minutes.


Hence, one slower pump will do it in 7*216 minutes.


The faster tank will do it 6 times faster, i.e. in  {{{(7*216)/6}}} = 7*36 = 252 minutes.


You got the same answer as above.
</pre>

My congrats (!)


Now you know TWO METHODS to solve the problem.


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It is a standard and 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>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.