Question 1103790
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A plane travels at a speed of 205 MPH in still air. Flying with {{{highlight(cross(a_tailwind))}}} the wind, the plane is clocked over a distance of 950 miles. 
Flying against {{{highlight(cross(a_headwind))}}} the wind, it takes 2 hours longer to complete the return trip. what was the {{{highlight(cross(wind _velocity))}}} speed of the wind ?
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<pre>
Let v = the wind speed (in miles per hour), now unknown.


The  the tailwind speed = 205 + v miles per hour.

         Headwind speed = 205 - v miles per hour.


"Time equation"

{{{950/(205-v)}}} - {{{950/(205+v)}}} = 2  hours.

950*(205+v) - 950*(205-v) = 2*(205^2-v^2)

2*950*v = 2*(205^2-v^2),

950v = 205^2 - v^2

v^2 + 950v - 205^2 = 0

{{{v[1,2]}}} = {{{(-950 +- sqrt(950^2+4*205^2))/2}}} = {{{(-950 +- 1034.7)/2}}}.


Only positive root makes sense:  v =  {{{(-950 + 1034.7)/2}}} = 42.35 mph.


<U>Answer</U>.  The speed of the wind is 42.35 mph.
</pre>


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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.


In these lessons you will find the detailed solutions of many similar problems. 

Consider them as samples. &nbsp;Read them attentively.

In this way you will learn how to solve similar 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.