# Related rates, baseball diamond

1. ### rocomath

Even problem, very plz!

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 the first base?

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

Work for A:

Distance from each base is x, evaluate when x = 45 ft

The distance from the runner to 2nd base, is z

Using Pythagorean theorem:

$$2x^2=z^2$$

$$2x\frac{dx}{dt}=z\frac{dz}{dt}$$

$$2x\frac{dx}{dt}=x\sqrt 2\frac{dz}{dt}$$

$$\frac{dz}{dt}\approx -34.0 ft/s$$

I'm mainly concerned with the set up, same for B?

2. ### rootX

z = sqrt (90^2 + x^2)