Two lovers have a spat and swear they will never see each other again. The girl walks due south at 6 mph while the boy walks at 10 mph on a heading of North 60 degrees West. How fast is the distance between them changing 30 minutes later?

Answer 1

the distance z is found using

z^2 = u^2 + v^2 - 2uv cos 2pi/3

what are u and v? The girl's and boy's distances, where

u = -6t
v = 10t

z^2 = 136t^2 - 60t^2
z^2 = 76t^2

so, now you know you have to find z(1/2), and then use

z dz/dt = 152 t