Question 1141756
.
<pre>
Flying with the wind, their effective speed (the ground speed) was

    {{{1980/4.5}}} = 440 miles per hour.

This effective speed is the sum of the airplane speed "u" and the wind speed "v":

    u + v = 440.     (1)



Flying against the wind, their effective speed (the ground speed) was

    {{{1980/5.5}}} = 360 miles per hour.

This effective speed is the <U>DIFFERENCE</U> of the airplane speed "u" and the wind speed "v":

    u - v = 360.     (2)



Thus you have two equations (1) and (2) to determine two unknowns, u and v.


Add the equations (1) and (2), and you will get


    2u = 440 + 360 = 800  ====>  u = 800/2 = 400 mph.


It is the airplane speed at no wind.


Next, substitute the found value of   "u"  into equation (1) to find  "v"


    400 + v = 440  ====>  v = 440 - 400 = 40 mph.


<U>ANSWER</U>.  The airplane speed at no wind is 400 mph.  The wind speed is 40 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, 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.