# Homework Help: Related Rates street light shadow

1. Jun 30, 2008

### rocomath

A man standing 3 feet from the base of a lamppost casts a shadow 4 feet long. If the man is 6 feet tall and walks away from the lamppost at a speed of 400 feet per minute, at what rate will his shadow lengthen? How fast is the tip of his shadow moving?

I'm unsure of how to solve the 2nd part, a bump would be good. Kinda brain dead atm :)

Here's the first part: Just use similar triangles

$$\frac{z}{x+y}=\frac 6 y \ \ \ z=\frac{21}{2}ft$$

$$y=x\left(\frac{6}{z-6}\right)$$

$$\frac{dy}{dt}=\frac{dx}{dt}\left(\frac{6}{z-6}\right)=\frac{1600}{3}\frac{ft}{min}$$

2. Jun 30, 2008

### rocomath

Oh nvm, it's just the sum of the 2 rates ... brain dead :p