Answer
$v = 0.66~c$
Work Step by Step
We can find $\gamma$:
$\Delta t = \gamma~\Delta t_0$
$\gamma = \frac{\Delta t}{\Delta t_0}$
$\gamma = \frac{4~days}{3~days}$
$\gamma = 1.33$
We can find the speed relative to the space station:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$1-\frac{v^2}{c^2} = \frac{1}{\gamma^2}$
$\frac{v^2}{c^2} = 1-\frac{1}{\gamma^2}$
$v^2 = [1-\frac{1}{\gamma^2}~]~c^2$
$v = \sqrt{1-\frac{1}{\gamma^2}}~\times c$
$v = \sqrt{1-\frac{1}{1.33^2}}~\times c$
$v = 0.66~c$
