# Related rates of speed and distance

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A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s.

(a) At what rate is his distance from second base decreasing when he is halfway to first base?

(b) At what rate is his distance from third base increasing at the same moment?

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#### Solution Preview

Let u be the distance from 2nd base.

u=(90^2+x^2)^(1/2)

where x is the distance from 1st base

du/dt = x*[(90^2+x^2)^(-1/2)](dx/dt)

dx/dt = 24 ft/s (actually it should be negative, since the ...

#### Solution Summary

This shows how to find the rate of change of distance with a runner in a baseball diamond.

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