Question 1189753
.
An airplane travels 5096 kilometers against the wind in 7 hours 
and 5796 kilometers with the wind in the same amount of time. 
What is the rate of the plane 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 kilometers per hour), and
let v be the rate of wind.


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


From the condition, we have this system of equations


    u + v = 5796/7 = 828  km/h    (1)

    u - v = 5096/7 = 728  km/h    (2)


To solve the system, add the equations. You will get


    2u = 828 + 728 = 1556;  hence  u = 1556/2 = 778  km/h.


Then from equation (1),

    v = 828 - u = 828 - 778 = 50 km/h.


<U>ANSWER</U>.  The rate of the airplane in still air is 778 kilometers per hour;  
         the rate of the wind is 50 kilometers per hour.
</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.