So here I thought it might be something to formulate a triangle, or actually two:There is a lamp post 15 feet tall casting a shadow 'B' ft. long of a person that is 6 feet tall standing 'A' ft. from the lamp post. If the person moves away from the lamp post at 5 feet per second, how fast does the shadow lengthen?

So the problem is asking me to find the derivative of the shadow's length with respect to time: $\displaystyle \frac{dB}{dt}$

I think the triangles are similar:

$\displaystyle \frac{15}{A+B} = \frac{6}{B} \\

\\

\cdots

\\

B = \frac{2}{3}A$

So we have B and I will attempt to take the derivative of this:

$\displaystyle \frac{dB}{dt} = [\frac{2}{3}A]'$

Constant/Chain rules:

$\displaystyle \frac{dB}{dt} = \frac{2}{3} \cdot [A'] \\

= \frac{2}{3} \cdot \frac{dA}{dt}$

Now how do I find the derivative of 'A'? It must have something to do with the movement velocity because it was given information and I haven't used it yet. Unless I am being tricked and it is extraneous/unnecessary information.