SOLUTION: Two planes take off from an airport at the same time. They fly at right angles to each other and one hour later they are 390km apart. If one plane travels 210km/hr faster than the

Question 300752: Two planes take off from an airport at the same time. They fly at right angles to each other and one hour later they are 390km apart. If one plane travels 210km/hr faster than the other, what is the speed of the two planes?
I tried to apply Pythagoras Theorem, making the hypotenuse 390, and the sides x and x+210. I squared 390 = the sum of the squares of x and x+210, but my answers always come out wrong.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Two planes take off from an airport at the same time. They fly at right angles to each other and one hour later they are 390km apart. If one plane travels 210km/hr faster than the other, what is the speed of the two planes?
.
Let x = speed of slower plane
then
x+210 = speed of faster plane
.
x^2 + (x+210)^2 = 390^2
x^2 + (x+210)(x+210) = 390^2
x^2 + x^2+420x+44100 = 152100
2x^2+420x+44100 = 152100
x^2+210x+22050 = 76050
x^2+210x-54000 = 0
(x+360)(x-150) = 0
x={150, -360}
Throw out the negative:
x = 150 km/hr (slower plane)
.
faster plane:
x+210 = 150+210 = 360 km/hr
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