Question 1177337
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When a plane flies with the​ wind, it can travel 920 miles in 2 hours. 
When the plane flies in the opposite​ direction, against the​ wind, it takes 4 hours to fly the same distance. 
Find the rate of the plane in still air and the rate of the wind.
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<pre>
Let u be the rate of the plane at no wind (in miles per hour)
and v be the rate of the wind (in the same units).


Then the effective rate  of the plane with   the wind is u + v
and  the effective rate of the plane against the wind is u - v.


From the problem, the effective rate of the plane with the wind is the distance of 920 miles 
divided by the time of 2 hours  {{{920/2}}} = 460 mph.

                  The effective rate of the plane against the wind is the distance of 920 miles 
divided by the time of 4 hours  {{{920/4}}} = 230 mph.


So, we have two equations to find 'u' and 'v'

    u + v = 460,    (1)

    u - v = 230.    (2)


To solve, add equations (1) and (2).  The terms 'v' and '-v' will cancel each other, and you will get

    2u = 460 + 230 = 690  --->   u = 690/2 = 345.

Now from equation (1)

     v = 460 - u = 460 - 345 = 115.


<U>ANSWER</U>.  The rate of the plane in still air is 345 mph.  The rate of the wind is 115 mph km/h.
</pre>

Solved.


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This solution produces the same answer as in the post by @mananth, but has an advantage
that it does not contain excessive calculations that the solution by @mananth has.


We, the tutors, write here our solutions not only to get certain numerical answer.
We write to teach - and, in particular, to teach solving in a right style.


This style solving presented in my post, is straightforward with no logical loops.
The solution presented in the post by @mananth has two logical loops.


<pre>
    One loop in the @mananth post is writing

        d/r = t  --->  920/(x+y) = 2   --->   2x + 2y = 920  --->  /2  --->  x+y = 460,

    while in my solution I simply write for the effective rate 

        u + v = 920/2 = 460.


    Second loop in the @mananth post is writing

                       920/(x-y) = 4   --->   4x - 4y = 920  --->  /4  --->  x-y = 230,

    while in my solution I simply write for the effective rate upstream

        u - v = 920/4 = 230.
</pre>

It is why I presented my solution here and why I think it is better than the solution by @mananth:
- because it teaches students to present their arguments in a straightforward way, without logical zigzags.


@mananth repeats his construction of solution with no change for all similar problems on flies
with and against the wind simply because his COMPUTER CODE is written this way.
But this way is not pedagogically optimal - in opposite, it is pedagogically imperfect.