A baseball diamond is a square with side 90 feet. A batter hits the ball and runs to first base with a speed of 20 feet per second. At what rate is his distance from third base increasing when he is halfway to first base?
when he is x feet from home, the distance z to 3rd base is
z^2 = x^2 + 90^2
z dz/dt = x dx/dt
when x = 45, z = 45√5 so
dz/dt = 20/(45√5)