Question 1119713
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<pre>
Let u = rate of the plane in calm air, in miles per hour;

    v = rate of wind.


Then the effective speed flying with the wind is  {{{420/3}}} = 140 mph.

It is the sum u + v, so your first equation is

u + v = 140.    (1)



The effective speed flying against the wind is  {{{420/5}}} = 84 mph.

It is the difference u - v, so your second equation is

u - v =  84.    (2)


Thus you have the system of two linear equations (1) and (2).

To solve it, add the equations.  You will get


2u = 140 + 84 = 224  ====>  u = 224/2 = 112.


Then from equation (1)  v = 140 - 112 = 28.


<U>Answer</U>.  The rate of the plane in calm air is  112 miles per hour.

         The rate of the wind is 28 miles per hour.


<U>Check</U>.   Check the solution on your own.

         After doing it, you will understand the solution much better.
</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.