Solving triangles? 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

It sounds like there is a second part to this question based on the mention of her friend standing 16 feet away, but I will go ahead and answer the question with the information provided.

Initiall distance of tip of shadow from the post:

18 + 10 = 28 feet

Distance the woman moved:

3 * 4 = 12 feet

Final distance from the post of the woman from the post:

18 + 12 = 30 feet

call the final length of her shadow "x":

Final distance of tip of shadow from the post:

30 + x

The final product has two similar triangles.  Knowing that two similar triangle are proportional we know that:

(30+x)/14 = x/5

150 + 5x = 14x

9x = 150

x = 50/3 = 18.667

Distance that the tip of the shadow travelled is:

18.667 + 30 - 28 = 20.667

Average rate of shadow tip travel is:

20.667/4 = 5.1667 = 5 1/6 feet per second

Answer 2

let shadow's tip total distance be d.

x / 5 = (18 + 3*4 + x) / 14

x / 5 = (x + 30) / 14

14x = 5x + 150

9x = 150

x = 150 / 9 = 50 / 3

d = (x + 30) - (10 + 18)

= 50/3 + 2

= 56/3

average speed

= d / (4 seconds)

= 56 / 3*4

= 14 / 3

= 4.667 feet per second