Question 1050528
.
Flying with the wind, a plane flew 1200 mi in 5 h. Against the wind, the plane required 6 h to fly the same distance. 
Find the rate of the plane in calm air and the rate of the wind
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<pre>
From the condition, you have these two equations

{{{1200/5}}} = u + v,   (1)   (flying with wind, the equation for the speed)

{{{1200/6}}} = u - v.   (2)   (flying against the wind)

Here u is the plane speed at no wind, v is the wind speed.

Simplify the system (1), (2):

u + v = 240,      (3)
u - v = 200.      (4)

To solve it, add the equations (3) and (4). You will get

2u = 240 + 200  --->  2u = 440  --->  u = {{{440/2}}} = 220.

You just found the speed of the plane at no wind. It is 220 mph.

Now you can easily find v from (1): v = 240 - u = 240 - 220 - 20.

Thus the speed of the wind is 20 mph.

<U>Answer</U>.  Speed of the plane at no wind is 220 mph.  The speed of the wind is 20 mph.
</pre>

For more similar problems and more details related to solutions 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/More-problems-on-upstream-and-downstream-round-trips.lesson>More problems on upstream and downstream round trips</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-boat-floating-Upstream-and-Downstream.lesson>Selected problems from the archive on the boat floating Upstream and Downstream</A> 

in this site.


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 topic "<U>Travel and Distance problems</U>" of the section "<U>Word problems</U>".