The infield of a baseball field is a diamond that measures 90 feet on each side. A runner runs from first base to second base at the rate of 25 ft/sec. How fast is the runner moving away from home plate when he is 30 feet from first base?

If is the distance the runner travels between first and second base, then the distance between him and home plate satisfies

(where the 90 here refers to the distance between first base and home)

Differentiating both sides with respect to time gives

The runner's speed is . When he is away from first base, he is

away from home plate. So he is moving away from home plate at a rate of

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