Question 1136644
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<pre>
Let u be the airspeed of the airplane (in miles per hour), and

let v be the speed of the wind.



The speed of the airplane flying with the wind is (u + v); at the same time it is equal to  

    {{{1400/4}}} = 350 miles per hour.

So, your first equation is

    u + v = 350.      (1)



The speed of the airplane flying againt the same wind is (u - v); at the same time it is equal to  

    {{{1400/ 4&42/60}}} = {{{1400/((282/60))}}} = {{{1400/((47/10))}}} = {{{14000/47}}} miles per hour.

So, your second equation is

    u - v = {{{14000/47}}}.    (2)



Add equations (1) and (2). You will get


    2u = {{{14000/47 + 350}}} = {{{(14000 + 47*350)/47}}} = 647.872  =====>  u = {{{647.872/2}}} = 323.936 miles per hour.


Substitute this value of "u" into the equation (2) to get v = 350-u = 26.064.


<U>ANSWER</U>.  The airspeed of the plane is  323.936 miles per hour;  the speed of the wind is  26.064 miles per hour.
</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.