Question 1125422
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<pre>
The airplane effective speed, when flying into a head wind, is  {{{1575/4.5}}} = 350 mph. 
This speed is the difference  u-v  of the airplane speed in still air and the wind speed:  u - v = 350 mph.


The airplane effective speed, when flying with the wind, is  {{{1575/3.5}}} = 450 mph.
This speed is the sum u+v of the airplane speed in still air and the wind speed: u + v = 450 mph.


To determine the airplane speed in still air  "u"  and the wind speed  "v", you need to solve this system of two equations:

u - v = 350,   (1)
u + v = 450.   (2)


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

2u = 350 + 450
2u = 800,

u = {{{800/2}}} = 400 miles per hour.  It is the airplane speed in still air.

Then from (1) you find  v = u - 400 = 450 - 400 = 50 miles per hour.  It is the wind speed.
</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.