Question 1117087
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<pre>
Let v be the rate of the jet stream, in miles per hour.


Then the effective speed of the plane flying with the wind is (520+v) mph, and the time of the flight with tailwind is {{{1600/(520+v)}}} hours.


    The effective speed of the plane flying against the wind is (520-v) mph, and the time of the flight with headwind is {{{1600/(520-v)}}} hours.


The time difference is  {{{1/2}}}  of an hour,  which gives you an equation

{{{1600/(520-v)}}} - {{{1600/(520+v)}}} = {{{1/2}}}.


To solve it, multiply both sides by  2*(520-v)*(520+v).  You will get

2*1600*(520+v) - 2*1600*(520-v) = (520-v)*(520+v)

2*1600*v + 2*1600*v = 520^2 - v^2

v^2 + 6400v = 520^2

v^2 + 2*3200 + 3200^2 = 520^2 + 3200^2

{{{(v + 3200)^2}}} = 10510400

v + 3200 = +/- {{{sqrt(10510400)}}}

v = - 3200 + 3241.975 = 41.975.


<U>Check</U>.  {{{1600/(520-41.975)}}} - {{{1600/(520+41.975)}}} = 0.5.   ! Correct !


<U>Answer</U>.  The rate of the jet stream was  41.975 mph.
</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, 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.



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I agree with the @Alan's note that the geographical settings in this problem are FAR from to be perfect.