500 mph is the speed of the plane.
This creates a right triangle, with the distance between the plane and the radar station serving as the hypotenuse (s). Let y represent the plane's height and x represent its flight route.
s2 = y2 + x2
Given: the constant value of y = 6
negative since decreasing, ds/dt = -400
Trying to locate dx/dt
Taking the implicit derivative of the above equation's two sides
0 + 2xdx/dt = 2sds/dt
(S/X) ds/dt = dx/dt
When x = 8
s = √(62+82) = √100 = 10
dx/dt = (10/8)(-400) = -500 mph, or 500 mph traveling toward the radar station at a distance of 6 miles.
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