Answer
The linear speed with which the bucket moves down the well is $0.3m/s$
Work Step by Step
The crank handle has tangential speed $v_T=1.2m/s$ and radius $r=0.2m$. Its angular speed is $$\omega=\frac{v_T}{r}=6rad/s$$
This angular speed of the handle is also the angular speed of the barrel of the crank. The barrel has a radius $r=0.05m$, so its tangential speed is $$v_T=\omega r=0.3m/s$$
This is also the linear speed with which the bucket moves down the well.
