Question 1129775
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<pre>
Let x be the boat speed in still water, in km/h.


Then your "time" equation is


{{{8/(x-3)}}} + {{{8/(x+3)}}} = 2   hours.


8*(x+3) + 8*(x-3) = 2*(x+3)*(x-3)

8x + 24 + 8x - 24 = 2*(x^2-9)


16x = 2x^2 - 18


2x^2 - 16x - 18 = 0

x^2 - 8x - 9 = 0

{{{x[1,2]}}} = {{{(8 +- sqrt(8^2 + 4*9))/2}}} = {{{(8 +- sqrt(100))/2}}} = {{{4 +- 5}}}.


Only positive root  x = {{{4 + 5}}} = 9 km/h  is meaningful. 


<U>Check</U>.  {{{8/(9+3)}}} + {{{8/(9-3)}}} = {{{8/12 + 8/6}}} = {{{8/12 + 16/12}}} = {{{24/12}}} = 2  hours.   ! Correct !


<U>Answer</U>.   The speed of the boat in still water is 9 km/h.
</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.