Question

A street light is at the top of a "20" ft tall pole. a woman "6" ft tall walks away from the pole with a speed of "5" ft/sec along a straight path. how fast is the tip of her shadow moving when she is "50" ft from the base of the pole?

Answer 1

Height of Woman, w = 6 ft. 
Distance Between Woman and Pole, s = 35 ft. 
Speed of Woman, ds/dt = 5 ft./sec 
Length of Shadow = L 
Distanc Between Woman and End of Shadow = x 
p / (s + x) = w / x 
13 / (35 + x) = 6 / x 
13x = 6(35 + x) 
13x = 210 + 6x 
13x - 6x = 210 
7x = 210 
x = 210 / 7 
x = 30 

L = s + x 
L = 35 + 30 
L = 65 

p / L = w / (L - s) 
13 / L = 6 / (L - s) 
13(L - s) = 6L 
13L - 13s = 6L 
13L - 6L = 13s 
7L = 13s