Answer
$-\frac{11\pi}{360}rad/min=-5.5^{\circ}/min$
Work Step by Step
Step 1. The minute hand moves $2\pi$ in $60$min; thus $\frac{d\theta_1}{dt}=\frac{2\pi}{60}=\frac{\pi}{30}$ rad/min
Step 2. The hour hand moves $2\pi$ in $12(60)$min; thus $\frac{d\theta_2}{dt}=\frac{2\pi}{12(60)}=\frac{\pi}{360}$ rad/min
Step 3. The rate of changing is the difference: $|\frac{d\theta}{dt}|=|\frac{\pi}{30}-\frac{\pi}{360}|=\frac{11\pi}{360}rad/min=5.5^{\circ}/min$
Step 4. At 4pm, the minute hand will try to catch up with the hour hand, so the angle is decreasing, which gives
$\frac{d\theta}{dt}=-\frac{11\pi}{360}rad/min=-5.5^{\circ}/min$
