Calculus rates
posted by Sarah .
A man 6ft. tall walks at the rate of 5 ft/sec toward a streelight that is 16 ft. above the ground. At what rate is the length of his shadow changing when he is 10ft. from the base of the light?

x is shadow tip from streetlight
y is man from streetlight
from similar triangles
x/16 = (xy)/6
16 x  16 y = 6 x
16 y = 10 x
x = 1.6 y
dx/dt = 1.6 dy/dt
= 1.6*5