Question 117642
After a lot of tough calculations, I get {{{w = 164.065}}} for
the windspeed. Plugging it back into the formula, it seems
to check OK.
The formula I used is:
{{{(733 / (224 - w)) + (1075 / (224 + w)) = 15}}}
I multiply both sides by {{{224 - w}}}
{{{733 + 1075*((224-w)/(224+w)) = 15(224-w)}}}
{{{1075*((224-w)/(224+w)) = 15(224-w) - 733}}}
{{{1075*(224-w) = (224+w)*(3360 - 15w -733)}}}
{{{240800 - 1075w = (224+w)(2627 - 15w)}}}
{{{240800 - 1075w = 588448 + 2627w - 3360w - 15w^2}}}
{{{-15w^2 + 3702w -3360w -240800 + 588448 = 0}}}
{{{-15w^2 + 342w + 347648}}}
Using the quadratic equation
{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{w = (-342 +- sqrt( 342^2-4*(-15)*347648 ))/(2*(-15)) }}}
{{{w = (-342 +- sqrt( 116964 + 20858880)) / -30}}}
{{{w = (-342 +- sqrt(20975844)) / -30}}}
{{{w = (-342 +- 4579.9393) / -30}}}
I want a positive result for the windspeed, so I must
have a negative result in the numerator because -/- = +
{{{w = (-4921.93930) / -30}}}
{{{w = 164.0646}}} mi/hr windspeed
check answer
{{{(733 / (224 - w)) + (1075 / (224 + w)) = 15}}}
{{{(733 / (224 - 164.0646)) + (1075 / (224 + 164.0646)) = 15}}}
{{{733 / 59.93536) + (1075 / 388.0646) = 15}}}
{{{12.22984 + 2.770157 = 15}}}
{{{14.99999734 = 15}}}
close enough