Solving triangles, please help! URGENT!!!!?

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 6 foot tall 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

You know that her shadow moved for 4 seconds, so all you need to find the rate of speed is her shadow's length.  

4 seconds at 3 f/s means she moved 12 feet, so at the end of her walk she is 30 feet away from the pole.  Imagining that the pole is the y-axis, and the ground is the x-axis, the top of the woman's head is at (30,5) at the end of her walk and the top of the pole is at (0,14).  So, the tip of her shadow should end up at the x-intercept of a line going through (30,5) and (0,14).  You can put it in y = mx +b if you find the slope; you already know "b", the y-intercept, to be 14, so all you need is the slope, m.  slope = (y2-y1)/(x2-x1), or (5-14)/(30-0), or -3/10.  So, find the x-intercept for the equation y = -3x/10 + 14.  To find the x intercept, set y equal to 0.  

0 = 14 - 3x/10

3x/10 = 14

3x = 140

x = 46 2/3

The tip of her shadow is 46 2/3 ft away from the pole, and it started out 28 feet from the pole.  That means it moved 18 2/3 feet in 4 seconds.

d = rt

18 2/3 = 4r

(140/3)(1/4) = r

140/12 = r

r = 35/3 = 11 1/3 f/s

The tip of her shadow is moving at a rate of 11 1/3 ft/sec.

Answer 2

The total distance the woman walks is

4 second * 3 ft/sec = 12 feet

Too find out where the shadow ends, I'm going to create an equation and solve for when it hits the y axis.

y = mx + b

b = 14

m = (5-14) / (30-0) = -9/30

y = (-9/30) x + 14

0 = (-9/30) x + 14

x = 46 + 2/3

Her shadow's length when finished is

46 + 2/3 - 30 = 16 + 2/3

The average speed of the shadow is then:

(16 + 2/3 - 10)ft / 3 sec

= 2.222 feet / second

Answer 3

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