Question

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

let the time after their split be t hrs
I see a triangle with sides 10t and 6t and an angle of 120° between them
let the distance between them be d miles

by the cosine law:

d^2 = (6t)^2 + (10t)^2 - 2(6t)(10t)cos120°
= 136t^2 + 60t^2

d2 = 196t^2
d = 14t
dd/dt = 14 mph , a rate independent of the time

check my arithmetic

Answer 2

You don't have to derive anything?