Question 1103620
.
An aircraft flew 4 hours with the wind. The return trip took 5 hours against the wind. If the speed of the plane in still air 
is 184 miles per hour more than the speed of the​ wind, find the wind speed and the speed of the plane in still air.
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        In such/(in similar) problems the term "in still water" is commonly accepted;


        but the term "in still air" is NEVER used.


        Instead, the term "at no wind" is used.



<pre>
Let  "u"  be the aircraft speed at no wind (in miles per hour),  and
let  "v"  be speed of the wind.


Then the aircraft tailwind speed is (u+v) mph,
while the aircraft speed against the wind is (u-v) mph, which is exactly 184 mph.


Therefore, the one-way distance aircraft covered flying against the wind was 

184*5 = 920 miles.


Hence, flying tailwind, the aircraft tailwind speed was  u+v = {{{920/4}}} = 230 mph.


Now you have these two equations

u + v = 230,    (1)
u - v = 184.    (2)     (given).
----------------------------------------Add the equations (both sides). You will get

2u = 230 + 184 = 414  ====>  u = {{{414/2}}} = 207.


Then from eq(1),  v = 230 - 207 = 23.


<U>Answer</U>.  The aircraft speed at no wind is  207 mph.   The speed of the wind is  23 mph.
</pre>


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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.


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

Consider them as samples. &nbsp;Read them attentively.

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



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.