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

the shadow's tip moves at 10 feet per second

set ratios of similar right triangle sides equal

20/6 = 10/3 = T/(T-35)

3T = 10T-350

7T = 350

T =50 feet in 5 seconds

50/5 = 10 feet per second = Tip's speed