Question 1115209
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<pre>
{{{1200/(300-r)}}} - {{{1200/(300+r)}}} = {{{3/2}}}


2400*(300+r) - 1200*(300-r) = 3*(90000-r^2)


4800r = 3*(90000-r^2)


1600r = 90000 - r^2


r^2 + 1600r - 90000 = 0.


{{{r[1,2]}}} = {{{(-1600 +- sqrt(1600^2 + 4*90000))/2}}} = {{{(-1600 +- 1708.8)/2}}}.


The positive solution is  r = 54.4.


<U>Answer</U>.  54.4 miles per hour.


<U>Check</U>.   {{{1200/(300-54.4) - 1200/(300+54.4)}}} = 1.5 hours.    ! Correct !
</pre>

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It is a typical and standard "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.