Street light Calculus Problem

Question

A street light is at the top of a 20-ft-tall pole. A 6-ft tall woman walks away from the pole with a speed of 7 ft/sec along a straight path (see figure). How fast is the tip of her shadow moving, in ft/sec, when she is 35 ft from the base of the pole?

Answer 1

a 6 foot tall woman moves at 7 feet per second away from the base of a 20 foot tall pole with a street light on top.

when she has walked 35 feet, 5 seconds have passed. 35/7 = 5

20/6 = T/(T-35) where T = the distance the shadow's tip moved

cross multiply

6T = 20T -700

14T =700

T = 50 feet in 5 seconds

50/5 = 10 feet per second = speed of the shadow's tip