Question

A clock has hands 1 and 1 3/5 inches long respectively. At what rate are the ends of the hands approaching each other when the time is 2 o'clock?

Answer 1

with the center of the clock at (0,0), the distance z between the tips at t minutes after 12:00 is

z^2 = m^2+h^2
z dz/dt = m dm/dt + h dh/dt

m = 8/5 cos(π/30 t)
h = cos(π/360 t)

Now just plug in the numbers at t=120

Answer 2

sorry about z. It is really found using the law of cosines

z^2 = (8/5)^2 + 1^2 - 2(8/5)cosθ
where θ is the angle between the hands. I'm sure you can figure that out.