Question 966100
r=215 miles per hour, speed without wind
w= unknown wind speed
v=750 miles
u=540 miles
t=amount of time, same for both trip situations


This is analyzed and solved purely symbolically because other questions have occurred like this but with different values or different examples of this same form.



_____________________rate___________time___________distance
WITHWIND_____________r+w_____________t______________v
AGAINSTW_____________r-w_____________t______________u


The variables w and t can be solved; but the question asks for w.


{{{system((r+w)t=v,(r-w)t=u)}}}



{{{t=v/(r+w)}}}
-


{{{r-w=u/t}}}


{{{r-w=u/(v/(r+w))}}}


{{{r-w=u(r+w)/v}}}


{{{(r-w)v=u(r+w)}}}


{{{rv-vw=ru+uw}}}


{{{rv-ru=vw+uw}}}


{{{rv-ru=w(u+v)}}}


{{{w=(rv-ru)/(u+v)}}}


OR


{{{highlight(w=(rv-ru)/(v+u))}}}