Cheating relativistically

Assume that the radio transmission (which travels at the speed of light), is sent at time $t_0$ in the frame in which the exam is taking place. From the point of view of this frame, the time $t$ at which the signal is received (after the exam begins), satisfies this equation:

$c(t - t_0) = vt \ \Rightarrow \ t_0 = \frac{t (c - v)}{c}$

The person moving away from the exam is recording proper time $\tau$ . We then know that:

$t = \frac{\tau}{\sqrt{1 - \frac{v^2}{c^2}}}$

We can then substitute this into the first equation to find $t_0$ :

$t_0 = \frac{\tau (c - v)}{c \sqrt{1 - \frac{v^2}{c^2}}} = \sqrt{\frac{1 - \frac{v}{c}}{1 + \frac{v}{c}}} \tau = \sqrt{\frac{2/5}{8/5}} (3 \ \text{hr}) = \boxed{1.5 \ \text{hr}}$