Question 1158426
.
<pre>

Let x be the spreed of the boat in still water, in kilometres per hour..

Then the speed downstream is (x+5) kilometres per hour, and the time traveled downstream is  {{{2/(x+5)}}} hours.

The speed upstream is (x-5) miles per hour, and the time traveled upstream is  {{{2/(x-5)}}} hours.


The total time equation is

   {{{2/(x+5)}}} + {{{2/(x-5)}}} = 4


Cancel the factor 2 in both sides


   {{{1/(x+5)}}} + {{{1/(x-5)}}} = 2


Multiply both sides by (x+5)*(x-5); then simplify


    (x-5) + (x+5) = 2*(x^2-25)

    2x            = 2x^2 - 50

    2x^2 - 2x - 50 = 0

    x^2  -  x  - 25 = 0

     {{{x[1,2]}}} = {{{(1 +- sqrt(1 + 4*25))/2}}} = {{{(1 +- sqrt(101))/2}}} = {{{(1 +- 10.05)/2}}}.


Only positive root  x = {{{(1 + 10.05)/2}}} = 5.525 is the solution.


<U>ANSWER</U>.  The speed of the boat in still water is 5.525 kilometres per hour.

<U>CHECK</U>.   {{{2/(5.525+5)}}} + {{{2/(5.525-5)}}} = 4 hours.   ! Correct !
</pre>

Solved.


-----------------


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.