Solving triangles, please help?

Question

A light, on top of a post, is 14 feet above the ground. At night a 5 foot woman is standing 18 feet from the post. The woman's shadow is 10 feet long. Her friend is standing 16 feet away from the post.

Starting 18 feet from the post, the woman walks directly away from the post for 4 seconds at a rate of 3 feet per second. Find the average speed(average speed = total distance/total time) on the tip of her shadow during that 4 second interval

http://i37.tinypic.com/2us8y7s.jpg

How do i solve this...

Answer 1

This can be solved by using the ratios of sides of triangles.

Note that (lightpost/base of lightpost/end of shadow) forms

a large triangle and that (woman's head/woman's feet/end of

shadow) forms a smaller, similar triangle.

In similar triangles, the ratios of similar sides are equal.

Let x = length of shadow.

At the start : 5 / 14 = x / (18 + x)

Solving this gives x = 10 feet, which you've already stated.

So tip of shadow is 18 + 10 = 28 feet from the post.

After 4 seconds, the woman will be 18 + 4*3 = 30 feet

from the post. Again, let x = length of shadow.

From similar triangles, we now get : 5 / 14 = x / (30 + x)

Solving gives x = 50/3 feet.

Therefore, tip of shadow is 30 + 50/3 feet from the post.

So the total distance the tip of the shadow has traversed is :

(30 + 50/3) - (28) = 56/3 feet. Total time is 4 seconds.

Thus, average speed = (56/3) / 4 = 14/3 feet per second.

I'm not sure why the woman's friend is there, but the

numbers given for the friend cannot be correct.