Question 1103240
{{{system(r=180,d=900,h=2,w=unknownWindSpeed)}}}
h is for time difference

<pre>
                  SPEEDS   TIMES      DISTANCE

WITH WIND          r+w     d/(r+w)      d

AGAINST WIND       r-w     d/(r-w)      d

DIFFERENCE                  h
</pre>

{{{highlight_green(d/(r-w)-d/(r+w)=h)}}}

Solve for w.

{{{d(r+w)-d(r-w)=h(r^2-w^2)}}}
{{{dr+dw-dr+dw=hr^2-hw^2}}}
{{{hw^2+2dw-hr^2=0}}}

Using general solution for quadratic equation, and not assuming the quadratic would be factorable,


{{{w=(-2d+- sqrt((2d)^2+4h*hr^2))/(2h)}}}


{{{w=(-2d+- sqrt(4d^2+4h^2r^2))/(2h)}}}


{{{highlight(w=(-d+- sqrt(d^2+h^2r^2))/h)}}}-------the PLUS form will probably be what you want.  Substitute the given values now and evaluate both solutions for w, and decide which makes sense.


Substitute the given values into the formula for w, and should find {{{highlight(w=34.7*(miles/hour))}}}.