Question 1035209
So typical a type of travel rate exercise that this solution will be all in symbols, and will work for ALL of this type of exercise.



Known variables,  h,d,k
Time with wind, h
Time against wind, k
Distance one way for trip, d


Unknown variables, r,w
Air speed for plane absent any wind, r
Speed of wind, w

<pre>
                 RATE       TIME    DISTANCE
WITHWIND         r+w          h       d
AGAINSTWIND      r-w          k       d
</pre>

Starting System of Equations:  {{{system((r+w)h=d,(r-w)k=d)}}}

Solve this system for r and w.


{{{system(rh+wh=d,rk-wk=d)}}}

{{{rh=d-wh}}}
{{{r=(d-wh)/h}}}-----*  and you might return to this formula later.
-
{{{((d-wh)/h)k-wk=d}}}

{{{(dk-whk)/h-wk=d}}}

{{{dk-whk-whk=dh}}}

{{{-2whk=dh-dk}}}

{{{2whk=dk-dh}}}


{{{highlight(w=(dk-dh)/(2hk))}}}


Use w to determine value for r.
{{{r=(d-wh)/h}}}
{{{r=(d-((dk-kh)/(2hk))h)/h}}}
{{{r=(d-(dk-kh)/(2k))/h}}}
{{{r=d/h-(dk-hk)/(2kh)}}},   LCD is 2kh;
{{{r=(d/h)(2k)/(2k)-(dk-hk)/(2kh)}}}
{{{r=(2dk-(dk-hk))/(2kh)}}}
{{{r=(2dk-dk+hk)/(2kh)}}}
{{{r=(dk+hk)/(2kh)}}}
{{{highlight(r=(d+h)/(2h))}}}