Question 978271
O'Hare is at the right angle of the right-triangle.

Northbound, (r+50)*3
Eastbound, r*3
{{{((r+50)*3)^2+(r*3)^2=240}}}


{{{3(r^2+100r+2500)+9r^2=240^2}}}
{{{r^2+100r+2500+3r^2=80*240}}}
{{{4r^2+100r+2500-80*240=0}}}

{{{4r^2+100r-167000=0}}}

{{{r^2+25r-4175=0}}}



Not trying to check factorization of 4175,
using discriminant instead,
discrim is {{{25^2-4*(-4175)=25^2+4*4175=17325=25*693=25*9*77=25*9*7*11}}};


{{{r=(-25+sqrt(25*9*77))/2}}}


{{{highlight(r=(-25+15*sqrt(77))/2)}}}
which is about 53.3 miles per hour for the east-bound plane.