Related Rates and Baseball?!?

Question

A baseball diamond has the shape of a square with sides 90 feet long. A player hits the ball and runs toward first base with a speed of 24 feet per second. At what rate is the player’s distance s from third base changing when the player is halfway to first base?

someone please explain this in a way thats easy to understand!
:]

Answer 1

Let
y = distance from home to runner
z = distance from runner to third base

Given:
dy/dt = 24 ft/sec

Find:
dz/dt when y = 45 ft

Form a right triangle between home plate, the runner, and third base.

z² = 90² + y² = 8100 + y²
2z(dz/dt) = 2y(dy/dt)
z(dz/dt) = y(dy/dt)

dz/dt = (y/z)(dy/dt) = 24y/z
dz/dt = 24*45/√(90² + 45²) = 24*45/[45√(4 + 1)]
dz/dt = 24/√5 ≈ 10.733126 ft/sec

The distance between the runner and third base is increasing at about 10.73 ft/sec.