Linear speed word problem

[RHSLilSweetie07]

Two pulleys have radii of 15 cm and 8 cm, respectively. The larger pulley rotates 25 times in 36 sec. Find the angular speed of each pulley in radians per second.

There are several formulas given:
omega = theta/time (for angular speed),
v (speed) = arc length/time,
v = (r*theta)/t, and
v = r*omega (all for linear speed).

I assume I use the 1st formula, omega = theta/time.
I found that the angular speed for the larger pulley is 25pi/18 radians per second.
I'm not sure how to find the angular speed for the smaller pulley. I know theta is equal to 16pi, but I don't know how to find time. Please help me.

 

[tkhunny]

Are the pulleys attached by a belt? Linear velocity must be the same.

Larger pulley moves (15 cm*2*pi*25)/(36 sec)
Smaller pulley moves (8 cm*2*pi*x)/(36 sec)

Find x.