How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?

Question

A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?

Answer 1

From similyarity of triangles we have 15/6 = (6t + x)/x; 5x = 12t + 2x; x = 4t. So dx/dt = 4 ft/s.

Tip of shadow moving with constant velocity 4 ft/s any time.