Question

A person whose height is 6 feet is walking away from the base of a streetlight along a straight path at a rate of 4 feet per second. If the height of a streetlight is 15 feet, what is the rate at which a person’s shadow is lengthening?

Answer 1

Let the distance from the pole be x and the length of the shadow be s. Using the law of similar triangles, we have:
s/6=(x+s)/15
thus
5s=2x+2s
3s=2x

hence
ds/dt=2/3 dx/dt
but
dx/dt=4 ft per second
hence
ds/dt=2/3*4=8/3