Question 1116842
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<pre>
The "time" equation is


{{{300/(125+w)}}} + {{{300/(125-w)}}} = 5    hours.    (1)


Solve for w, the rate of wind.


<U>Answer</U>.  Rate of wind is 25 miles per hour.
</pre>

I solved it mentally &nbsp;&nbsp;(since the answer is OBVIOUS).   &nbsp;&nbsp;//   &nbsp;&nbsp;The formal solution is as follows.


<pre>
    Multiply both sides of (1) by (125+w)*(125-w). You will get


    300*(125-w) + 300*(125+w) = 5*(125-w)*(125+w)

    60*(125-w) + 60*(125+w) = (125-w)*(125+w)

    2*60*125 = {{{125^2 - w^2}}}

    {{{w^2}}} = {{{125^2-2*60*125}}} = 125*(125-120) = 125*5 = {{{5^4}}}.

    w = {{{5^2}}} = 25.


    <U>Check</U>.  {{{300/(125+25)}}} + {{{300/(125-25)}}} = {{{300/100}}} + {{{300/150}}} = 3 + 2 = 5  hours.   ! Correct !
</pre>

Solved.


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It is a typical "tailwind and headwind" word problem.


See the 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/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/Selected-problems-from-the-archive-on-a-plane-flying-with-and-against-the-wind.lesson>Selected problems from the archive on a plane flying with and against the wind</A> 

in this site.



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.