Rate of change problem very hard

[arpitm08]

Rate of change problem...very hard...please help!

Homework Statement

The hands on a clock are of length 5 inches(minute hand) and 4 inches(hour hand). How fast is the distance between the tips of the hands changing at 3:00?

The Attempt at a Solution

Let the coordinates of the two hands be (x1,x2) for the minute hand, and (y1,y2) for the hour hand. Then,

s(distance) = sqrt((x2-y2)^2 + (x1-y1)^2)

Also,

25=(x1)^2 + (x2)^2
16=(y1)^2 + (y2)^2

Then ds/dt = (-2(x1 - x2y1/y2)dy1/dt - 2(y1 - y2x1/x2)dx1/dt)/sqrt((x2-y2)^2+(x1-y1)^2).
But I don't know how to calculate these rates.

Please Help!

 

[jhicks]

The problem involves things in a circular motion. I would convert x and y into parametric values involving sine and cosine with an angular velocity. That should tell you all those rates you don't know.