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**[SOLVED] Related Rates**

**1. Homework Statement**

Two aircraft are in the vicinity of a control center. Both are at the same altitude. Plane 1 is 36 nautical miles from the center and approaching it at a rate of 410 knots. Plane 2 is 41 nautical miles from the center and approaching it at a rate of 455 knots. (One knot is 1 nautical mile per hour)

A) How close will the planes come to eachother?

B) How many minutes before the time of closest approach?

**3. The Attempt at a Solution**

I can't figure out how to solve this... I keep getting stuck here is what I have done.

[tex] P_1(t)^2 + P_2(t)^2 = D(t)^2[/tex]

take the derivative

[tex] 2P_1(t)P_1'(t) + 2P_2(t)P_2'(t) = 2D(t)D'(t) [/tex]

and then the place where the distance would be a minimum is where D'(t) = 0, but I keep getting stuck here because I don't know either of the two P(t)s. Can someone please help me set this problem correctly? Thanks