On a certain clock the minute hand is 4 in long and the hour hand is 3 in long. how fast is the distance between the tips of the hands changing at 4 pm?

The correct answer is 70.95 inches/hour.
To solve this, 
The minute hand is rotating at 2pi rad/hour 
The hour hand is rotating at 2pi/12 or pi/6 rad/hour 
then dα/dt = pi/6 - 2pi = -11pi/6 rad/hour,
α = angle between the two arms 

let x - distance between the arms 
x^2 = 4^2 + 3^2 - 2(3)(4)cosα 
x^2 = 25 - 24cosα 

2x(dx/dt) = -24(-sinα)dα/dt 
dx/dt = 12(sinα)(dα/dt)/x 

4 pm:
α = 120º, sinx = 1/2 and cosα = √/3 

x^2 = 25 - 24(√3/2) 
x = 2.05314 
dx/dt = -12(1/2)(-11pi/6)/2.05314 
= -70.95 

Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help.