Question 1179658
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A plane traveling with the wind flew 1312.5 mi in 5.25 h. 
Against the wind, the plane required 6.25 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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        The solution in the post by @mananth is incorrect:  it has arithmetic errors.


        Not only is it technically unsuitable,  but it is also unsuitable in its design.


        In this my post,  I provide short and straightforward solution to the given problem.



<pre>
Let x be the rate of the plane in calm air, in miles per hour.

Let y be the rate of the wind.


Then  the effective speed of the plane with    the wind is (x+y) mph,

while the effective speed of the plane against the wind is (x-y) mph,



From the problem, the effective rate of the plane with the wind is  the distance divided by the travel time

    {{{1312.5/5.25}}} = 250 miles per hour,


and the effective rate of the plane against the wind is  the distance divided by the travel time

    {{{1312.5/6.25}}} = 210 miles per hour.


So, we have these two equations

    x + y = 250     (1)

    x - y = 210     (2)


To find x, add the equation.  You will get

    2x = 250 + 210 = 460,  x = 460/2 = 230.


Now express y from equation (1) and calculate

    y = 250 - x = 250 - 230 = 20.


At this point the problem is solved completely.


<U>ANSWER</U>.  The speed of the plane in calm air is 230 mph.  The rate of the wind is 20 mph.
</pre>

Solved.


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I placed this my solution here as an opposite alternative to the solution by @mananth.


Now I will explain you, why I think that my solution is better than that of @mananth.


The @mananth solution is more long way reasoning and calculations than it is necessary.
My solution is straightforward and contains only necessary reasoning and calculations.


    Everything which is not effective and straightforward, is filtered out.


The school education always prefers more straightforward and short reasoning, explanations and calculations,
because the goal of solving such problems is not only getting a correct answer.


A true goal of solving such problems is to teach students to organize 
and present their thoughts and their arguments in adequate form.


@mananth does it his way only because his computer code, which he permanently uses to create the solution file,
is written this way - but his way is not effective.



It is why I prepared and placed here my solution to provide a better way 
for you, a reader, to learn and to master this subject.



What I wrote here are not empty words.
Today, on Jan.21, 2026 I looked on how artificial intelligence treats this problem.
The Google AI Overflow repeats this long process, copying the style of @mananth.
Thus, thousands of schoolchildren will suffer and will not know how to correctly present 
their thoughts and how to correctly present a solutions to such problems.


And this is already a national-scale problem - when AI is copying from badly written sources.