Question 1137928
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<pre>
Let w be the wind velocity (in miles per hour).


Then the plane' speed with the wind is (175 + w) miles per hour,

and the time to fly 1000 miles with the wind is  {{{1000/(175+w)}}} hours.


Also, the plane' speed against the wind is (175 - w) miles per hour,

and the time to fly 1000 miles against the wind is  {{{1000/(175-w)}}} hours.


Now you can write the "time" equation


    {{{1000/(175-w)}}}  - {{{1000/(175+w)}}} = 1 hour


saying that  "it takes 1 hour longer to complete the return trip".


It is your basic equation.  To solve it, multiply both sides by (175+w)*(175-w).  You will get


    1000(175+w) - 1000(175-w) = 175^2 - w^2,   or


    2*1000*w = 175^2 - w^2

    w^2 + 2000w - 175^2 = 0

    {{{w[1,2]}}}  = {{{(-2000 +- sqrt(2000^2 + 4*175^2))/2}}} = {{{(-2000 +- 2030.394))/2}}}.


Only positive value of the roots is meaningful:  w = {{{(-200 + 2030.394)/2}}} = 15.197.


<U>ANSWER</U>.  The wind' speed is 15.197 miles per hour.


<U>CHECK</U>.  {{{1000/(175-15.197) - 1000/(175 + 15.197)}}} = 1 hour.   ! Correct !
</pre>


Solved, answered, checked and completed.


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



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.