



 
Hi Jonathan. It seems to me that this problem doesn't involve calculus, but rather just vectors. Allow me to explain.
The angular velocity of the ends of each hand are constant, so the tangential velocities are as well. To convert, we use the formula v = rω where v is the tangential (linear) velocity and ω is the angular velocity. Thus the tangential velocities are
The change in distance is simply the difference of these two vectors. If I reverse the minute vector so that I can add rather than subtracting vectors, I find a simple right triangle to solve: Since you are just interested in the speed the distance is changing, you just need to find the magnitude of R, which Pythagorus can help you with. Hope this helps,  


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