Answer
$s_B=8.25\times10^2m$
Work Step by Step
In the same amount of time, both chambers have the same angular displacement $\Delta\theta$ since they are connected to the same axis in the center.
The distance the astronaut has moved, which corresponds to $\Delta\theta$, is $$s=r\Delta\theta$$
So, $$\frac{s_B}{s_A}=\frac{r_B\Delta\theta}{r_A\Delta\theta}=\frac{r_B}{r_A}=\frac{1.1\times10^3m}{3.2\times10^2m}=3.4375$$ $$s_B=(2.4\times10^2m)\times3.4375=8.25\times10^2m$$
