Question 1000926
{{{system(r=unknownRate,w=unknownWindrate,t=timeWithWind,b=timeAgainstWind,d=distanceEachWay)}}}


Assigned Variable Values
{{{system(t=5,b=10,d=580)}}}
Think of t as  "to, with wind", and b as "back, against wind".

<pre>
           rate        time       distance
WITH       r+w          t         d
AGNST      r-w          b         d          
</pre>
Make the system of equations.
{{{system((r+w)t=d,(r-w)b=d)}}}


{{{system(rt+wt=d,rb-wb=d)}}}


{{{tw=d-tr}}}
{{{w=d/t-tr/t}}}
{{{w=d/t-r}}}
substitute,
{{{rb-(d/t-r)b=d}}}
{{{br-db/t+br=d}}}
{{{2br-db/t=d}}}
{{{2br=d+db/t}}}
{{{r=(d+db/t)/2b}}}
{{{r=(dt/t+db/t)/2b}}}
{{{r=(dt+db)/(2bt)}}}----you could use this form;
{{{highlight(r=d/(2b)+d/(2t))}}}----------plane speed absence of any wind, purely in symbols.


Now find wind speed.
{{{w=d/t-r}}}
{{{w=d/t-d/(2b)-d/(2t)}}},  simplest denominator is 2bt;
{{{w=(d/t)(2b/(2b))-(d/(2b))(t/t)-(d/(2t))(b/b)}}}
{{{highlight(w=(2bt-dt-db)/(2bt))}}}---------wind speed in purely symbolic form.


Substitute the given and known values to evaluate r and w.


You also have the answer to many other exercise questions which fit this same travel rates type, because it is solved in symbolic form; just the given values would be different but the same general description is often given.