
Related Rate Problem
Hey Guys. I'm correcting a Math test for extra points right now and I came across a question that I can't seem to figure out how to solve.
Anyone care to help?
Heres the problem:
A man 6 feet tall is walking at a rate of 5 ft/sec towards a light that is 20 feet above the ground. When he is 10 feet from the base of light, at what rate is the tip of his shadow changing.
I know how to draw the picture and thats about it haha. Where do I start?
Any help?
Thanks!
Aaron Snyder

let x = distance man is from the light
s = shadow length
using similar triangles from your sketch ...
$\displaystyle \frac{20}{x+s} = \frac{6}{s}$
$\displaystyle 3x = 7s$
you know $\displaystyle \frac{dx}{dt}$ ... find $\displaystyle \frac{ds}{dt}$
rate that the tip is moving is $\displaystyle \frac{d}{dt}(x+s)$

Thanks so much! I appreciate it! If only i had thought that the first time around! haha.

Quick question,
where did you get the 3x=7s from? I'm not seeing it right now.