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One airplane is approaching an airport from the north at 124 km/hr. A second airplane approaches from the east at 223 km/hr. Find the rate at which the distance between the planes changes when the southbound plane is 34 km away from the airport and the westbound plane is 15 km from the airport.

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Think of it as a triangle: one side has a length of 34 - 124x, and the other side has a length of 15- 223x. The distance between them is the hypotenuse of the triangle, while you find using Pythagorean theorem. Now that you have the equation for the distance, derive it, and that's it.
*which you can find, bahh typos.
\[r^2 = x^2 +y^2\] \[2r \frac{ dr }{ dt} = 2x \frac{ dx}{ dt} + 2y \frac{ dy}{ dt} \] \[ \frac{ dr }{ dt} =\frac{ 1 }{ r} (x \frac{ dx}{ dt} + y \frac{ dy}{ dt} )\]

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Other answers:

x=15 dx/dt = -223 y= 34 dy/dt = -124 r = sqrt(34^2 + 15^2)

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