SOLUTION: Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east. The northbound plane is flying 50 miles per hour faster than the eastbou

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Question 1066873: Two planes leave simultaneously from Chicago's O'Hare Airport, one flying due north and the other due east. The northbound plane is flying 50 miles per hour faster than the eastbound plane. After 3 hours the planes are 2320 miles apart. Find the speed of each plane. (Round your answers to the nearest whole number.)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
r, the speed of the eastward bound plane

North leg distance
%28r%2B50%29%2A3

East leg distance
r%2A3


%283r%2B150%29%5E2%2B9r%5E2=2320%5E2

9r%5E2%2B900r%2B22500%2B9r%5E2=2320%5E2

18r%5E2%2B900r%2B22500-5382400=0

18r%5E2%2B900r-5359900=0

9r%5E2%2B450r-2679950=0

r=%28-450%2Bsqrt%28450%5E2%2B4%2A9%2A2679950%29%29%2F18

r=%28-450%2Bsqrt%2896680700%29%29%2F18

r=%28-450%2B10%2Asqrt%28966807%29%29%2F18

r=%28-450%2B30%2Asqrt%28107423%29%29%2F18

r=%28-75%2B5%2Asqrt%28107423%29%29%2F3, 17*71*89 is the discriminant factored.

highlight%28r=84%29