Chapter 3: Derivatives - Section 3.8 - Related Rates - Exercises 3.8 - Page 163: 25

$20ft/s$

Step 1. See figure, $y=AB=300ft, s=OA=500ft$; we have $x^2=OB^2=500^2-300^2=400^2$ thus $x=400ft$ Step 2. With $\frac{dx}{dt}=25ft/s$, $\frac{dy}{dt}=0$, and $s^2=x^2+y^2$, we have $2s\frac{ds}{dt}=2x\frac{dx}{dt}$, thus $\frac{ds}{dt}=\frac{400}{500}\times25=20ft/s$