SOLUTION: FLYING SPEED:Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east (see figure).The northbound plane is flying 50 miles per hou

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Question 978271: FLYING SPEED:Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east (see figure).The northbound plane is flying 50 miles per hour faster than the eastbound plane.After 3 hours, the planes are 2440 miles apart.Find the speed of each plane.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
O'Hare is at the right angle of the right-triangle.
Northbound, (r+50)*3
Eastbound, r*3
%28%28r%2B50%29%2A3%29%5E2%2B%28r%2A3%29%5E2=240

3%28r%5E2%2B100r%2B2500%29%2B9r%5E2=240%5E2
r%5E2%2B100r%2B2500%2B3r%5E2=80%2A240
4r%5E2%2B100r%2B2500-80%2A240=0
4r%5E2%2B100r-167000=0
r%5E2%2B25r-4175=0


Not trying to check factorization of 4175,
using discriminant instead,
discrim is 25%5E2-4%2A%28-4175%29=25%5E2%2B4%2A4175=17325=25%2A693=25%2A9%2A77=25%2A9%2A7%2A11;

r=%28-25%2Bsqrt%2825%2A9%2A77%29%29%2F2

highlight%28r=%28-25%2B15%2Asqrt%2877%29%29%2F2%29
which is about 53.3 miles per hour for the east-bound plane.