Aman 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.

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