Question 1079094
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<pre>
{{{450/2}}} = u + v   (1)   is the equation for the effective speed of the plane flying with the wind.
{{{450/3}}} = u - v   (2)   is the equation for the effective speed of the plane flying against the wind.


Where u is the speed of the airplane at no wind, and v is the rate of the wind.


Or, equivalently,

u + v = 225,          (1')
u - v = 150.          (2')

Add equations (1') and (2') (both sides). You will get

2u = 225 + 150 = 375.

Hence, u = {{{375/2}}} = 187.5 miles per hour.


<U>Answer</U>.  The speed of the plane at no wind is 187.5 mph.
</pre>


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.


In these lessons you will find the detailed solutions of many similar problems. 

Consider them as samples. Read them attentively.

In this way you will learn how to solve similar problems once and for all.



Also, 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>", the topic "<U>Travel and Distance problems</U>".