Very confusing stuff?

Question

A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

Answer 1

I hope you drew a diagram. A problem like this is hard to do without one. Here's my diagram:

http://i17.tinypic.com/8e0xfn9.gif

AB denotes the pole with the street light at A, DE denotes the woman. Her distance from the pole is denoted by x; the length of her shadow is denoted by y. You are asked to find dy/dt when x=40, given that dx/dt=6.

Observe that right triangles ABC and DEC are similar. Corresponding parts of similar triangles are in proportion. So

(x+y)/10 = y/6

Solve that for y, then differentiate both sides with respect to time.