A man standing 9 feet from the base of a lamppost casts a shadow 6 feet long. if the man is 6 feet tall and walks away from the lamppost at a speed of 30 feet per minute, at what rate, in feet per minute, will his shadow lengthen?

Let x be the distance of shadow and y the distance of the man from the lampost

Height of lampost can be found using similar traingles and it comes to 15 feet.

x / (x + y) = 6/15 = 2/5

5x = 2x + 2y

3x = 2y

so y = (3/2) x and x = (2/3) y dy/dx = 3/2 and dx/dy = 2/3

speed at which y is increasing = dy/dt = 30

speed of shadow lengthening = dx / dt = dx/dy * dy/dt = 2/3 * 30 = 20 ft/min

Answer is 20 ft / minute.