At time t = 0, Santa is 200 feet directly overhead, and it seems that he is traveling at a constant speed and at a constant altitude. Ten seconds later, he is 825 feet away from you. How quickly is the distance between you and St. Nick changing at that instant?

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Begin by drawing a picture of the situation. A right triangle is formed between you and St. Nick. Therefore, your primary equation is 200² + d² = s². As Santa moves, d and s will change values, so you must leave those as variables. Now, take the derivative with respect to t. Since Santa is 825 feet away from you, that is the value for s at this instant. With this value (and 200) you can find d, with the Pythagorean Theorem; doing so gives you d = 800.3905297 feet. Furthermore, if it took him 10 seconds to travel that far, dd/dt must be 800.3905297/10, or 80.03905297 feet/sec. Now you have enough information to find ds/dt, what the problem actually asks for: Don't forget to include the units of ft/sec.