Question 1147334
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<pre>

If the speed of the current is "x" miles per hour, then


    - the effective rate of the motorboat upstream is   (24-x) mph, while

    - the effective rate of the motorboat downstream is (24+x) mph.



Then the time moving upstream is  {{{9/(24-x)}}}  hours, while

     the time moving downstream is  {{{9/(24+x)}}}  hours.



The total time is 1 hour, giving you this "time" equation

     {{{9/(24-x)}}} + {{{9/(24+x)}}} = 1  hour.



To solve it, multiply both sides by (24-x)*(24+x).  You will get

     9*(24+x) + 9*(24-x) = {{{24^2 - x^2}}}.


Simplify step by step

     9*24 + 9x + 9*24 - 9x = {{{24^2-x^2}}},

     2*9*24                = {{{24^2-x^2}}}

     {{{x^2}}} = {{{24^2 - 2*9*24}}} = 24*(24-2*9) = 24*6 = 12*12 = {{{12^2}}}.


It implies  x = {{{sqrt(12^2)}}} = 12.


<U>ANSWER</U>.  The speed of the current is 12 miles per hour.


<U>CHECK</U>.   {{{9/(24-12)}}} + {{{9/(24+12)}}} = {{{9/12}}} + {{{9/36}}} = {{{3/4}}} + {{{1/4}}} = 1 hour.    ! Precisely 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.