Question 1119371
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<pre>
Let "u" be the boat speed in still water, in miles per hour.


Then the boat' speed downstream is (u+2) miles per hour, while

     the boat' speed downstream is (u-2) miles per hour.


Time to travel downstream is {{{12/(u+2)}}} hours, while

time to travel upstream is  {{{12/(u-2)}}} hours.


The total time is  {{{12/(u+2)}}} + {{{12/(u-2)}}}  hours.


According to the condition, it is 5 hours, which gives you an equation

    {{{12/(u+2)}}} + {{{12/(u-2)}}} = 5.


To solve it, multiply both sides by (u+2)*(u-2) = (u^2-4).  You will get


    12*(u-2) + 12*(u+2) = 5*(u^2-4)


    12u - 24 + 12u + 24 = 5u^2 - 20,

    5u^2 - 24u - 20 = 0


    {{{u[1,2]}}} = {{{(24 +- sqrt(24^2 + 4*5*20))/(2*5)}}} = {{{(24 +- sqrt(976))/10}}}.


Only positive root works  u = {{{(24 + sqrt(976))/10}}} = 5.524.


<U>Answer</U>.  The boat' speed in still water is 5.524 miles per hour.


<U>Check</U>.   {{{12/(5.524+2) + 12/(5.524-2)}}} = 5.00 hours.   ! Correct !
</pre>

Solved.


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It is a typical and standard Upstream and Downstream round trip word problem.


You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems.lesson>Wind and Current problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Wind-and-Current-problems-solvable-by-quadratic-equations.lesson>Wind and Current problems solvable by quadratic equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Unpowered-raft-moving-downstream-along-a-river.lesson>Unpowered raft floating downstream along a river</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Selected-problems-from-the-archive-on-a-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> 

in this site, where you will find other similar solved problems with detailed explanations.


Read them attentively and learn how to solve this type of problems once and for all.


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 section "<U>Word problems</U>", &nbsp;the topic "<U>Travel and Distance 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.