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? 
.
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