Question

a man 6 feet tall is walking away from a lamp post at the rate of 60 feet per minute. when the person is 6 feet from the lamp post, his shadow is 12 feet long. find the rate at which the length of his shadow is increasing when he is 145 feet from the lamp post

Answer 1

If the light is at height h, we know that

6/12 = h/18
h = 9

So, if the shadow has length s when the man is x feet from the pole, then we have

s/6 = (x+s)/9
s = 2x
so, ds/dt = 2 dx/dt

Now just plug in your numbers.