Question 1185749
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Flying against the wind, an airplane travels 5390 kilometers in 7 hours. 
Flying with the wind, the same plane travels 3750 kilometers in 3 hours. 
What is the rate of the plane in still air and what is the rate of the wind?
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<pre>
Let  u  be the airplane rate in still air (in miles per hour), and
let  v  be the rate of the wind.


Then the airplane effective speed flying with the wind is  u+v  miles per hour,
while its effective speed flying against      the wind is  u-v  miles per hour.


From the condition, we have this system of equstions


    u + v = 3750/3 = 1250  mph    (1)

    u - v = 5390/7 =  770  mph    (2)


To solve equations, add them. You will get


    2u = 1250 + 770 = 2020;  hence  u = 2020/2 = 1010  mph.


Then from equation (1),

    v = 1250 - u = 1250 - 1010 = 240 mph.


<U>ANSWER</U>.  The rate of the airplane in still air is 1010 miles per hour;  the rate of the wind is 240 mph.
</pre>

Solved.



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<H3>Post-solution note</H3>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The rate of the wind seems  TOOOOO  high to be realistic.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is twice the air speed in the eye of an hurricane.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So keep in mind please that your input produces unrealistic output.


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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.