Answer
The astronaut would say that she exercises for 25.4 minutes.
Work Step by Step
Let $L_0 = 35.2~m$. The contracted length is $L = 30.5~m$. We can find $\gamma$:
$L = \frac{L_0}{\gamma}$
$\gamma = \frac{L_0}{L}$
$\gamma = \frac{35.2~m}{30.5~m}$
$\gamma = 1.154$
Let $\Delta t_0 = 22.2~min$. We can find $\Delta t$:
$\Delta t = \gamma~\Delta t_0$
$\Delta t = (1.154)(22.2~min)$
$\Delta t = 25.4~min$
The astronaut would say that she exercises for 25.4 minutes.
