Question 246104
Let x = air speed

250+x = speed with the wind
250-x= speed against the wind


Distance with the wind = Distance against the wind=576
{{{R*T[with]=576}}}
{{{T[with]=576/(250+x)}}}



{{{R*T[against]=576}}}
{{{T[against]=576/(250-x)}}}


TOTAL TIME = 5
{{{576/(250+x)+576/(250-x)=5}}}


Multiply both sides by (250-x)(250+x):

{{{576(250-x)+576(250+x)=5(250-x)(250+x)}}}

{{{576*250-576x+576*250+576x=5(62500-x^2)}}}

(I'm on vacation, and I don't have my calculator.  Use it if you have one!!)


{{{2*576*250=312500-5x^2}}}

{{{576*500=312500-5x^2}}}

{{{288000=312500-5x^2}}}
{{{5x^2=312500-288000}}}
{{{5x^2=24500}}}
{{{x^2 =4900}}}


{{{x= sqrt(4900)}}}, which I can do even WITHOUT a calculator!!!


{{{x= 70 }}} mph--a pretty strong wind!!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus