Question 1058812
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An airplane takes 3 hours to travel a distance of 1800 miles with the wind. The return trip takes 4 hours against the wind. 
Find the speed of the plane in still air and the speed of the wind.

I had a question about how would I have to set up this problem in order to find both my speeds? 
I have been stuck on this question for hours please, help!
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<pre>
{{{1800/3}}} = u + v   (1)  is the equation for the flight with the wind.
                      (Here "u" is the airspeed of the airplane with NO wind,
                            "v" is the wind speed)
{{{1800/4}}} = u - v   (2)  is the equation for the flight against the wind.


Simplify equations (1) and (2) and write them as a system:

u + v = 600,           (1')
u - v = 450.           (2')

Now add the two equations (1') and (2'). You will get

2u = 1050  --->  u = {{{1050/2}}} = 525 miles per hour.

Having this, you can easily determine "v" from (1'):  

v = 600 - 525 = 75 miles per hour.


<U>Answer</U>.  The plane airspeed  is 525 mph. The wind speed is 75 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.


You will find the detailed solutions of many similar problems there. 


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>".



If after reading my solution you still have a question "why the equations (1) and (2) have this form ?", 
then read the lessons above. They contain the detailed answer to this question.