Question 1045720
.
A man flies a small airplane a distance of 180 mi. Because he is flying into head wind, the trip takes him 2 hours. 
On the way back the wind is still blowing at the same speed so the return trip only takes 1 hr and 12 min. 
What is his speed in the still air? How fast is the wind blowing 
~~~~~~~~~~~~~~~~~~~~~~~


<pre>
When the man covered 180 mi in 2 hours flying into head wind, the speed of the plane relative to the ground was {{{180/2}}} = 90 mph. 

This speed is the difference of the plane speed in the still air "u" and the wind's speed "v":

{{{180/2}}} = 90 = u - v.     (1)

When the man covered the same distance of 180 mi in 1 hour 12 minutes in the return trip flying with the wind, 
the speed of the plane relative to the ground was {{{180/1.2}}} = 150 mph. 
Here 1.2 = 1.2 hour = 1 hour and 12 minutes.  (12 minutes = {{{1/5}}} hour = 0.2 hour).

This speed is the sum of the plane speed in the still air "u" and the wind's speed "v":

{{{180/1.2}}} = 150 = u + v.   (2)


So you have this two equations to find u and v:

u - v =  90    (1')   
u + v = 150.   (2')

The simplest way to solve this system is to add the equations (1') and (2').
If you do, you will get

2u = 90 + 150,  or  2u = 240.  Hence,  u = {{{240/2}}} = 120.

Thus the speed of the plane in the still air is 120 mph.

Having this, you can easily find the speed of the wind v from the equation (1'):

v = u = 90 = 120 - 90 = 30 mph.

<U>Answer</U>.  The speed of the plane is still air is 120 mph.
         The speed of the wind is 30 ph.
</pre>

Solved.


What I wrote here is the standard way of solving this type of problems and the standard way of explaining the solution.


For more solved problems of this type 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/Unpowered-raft-moving-downstream-along-a-river.lesson>Unpowered raft floating downstream along a river</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> 

&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.


Please be informed that 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>.