# Related Rate Problem

• Nov 2nd 2008, 01:50 PM
Fishkeeper101
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
• Nov 2nd 2008, 02:45 PM
skeeter
let x = distance man is from the light

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 $\displaystyle \frac{d}{dt}(x+s)$
• Nov 2nd 2008, 07:03 PM
Fishkeeper101
Thanks so much! I appreciate it! If only i had thought that the first time around! haha.
• Nov 2nd 2008, 09:23 PM
Fishkeeper101
Quick question,
where did you get the 3x=7s from? I'm not seeing it right now.