The definition of the invariant interval is
$\begin{align*}\left( \Delta s \right)^2 = \left(\Delta x \right)^2 + \left(\Delta y \right)^2 + \left(\Delta z \right)^2 - c^...$
First, we evaluate $\left( \Delta s \right)^2$ in inertial frame $S$ :
$\begin{align*}\left( \Delta s \right)^2 = 9 c^2 \;\mathrm{min}^2\end{align*}$
Now, we evaluate $\left( \Delta s \right)^2$ in inertial frame $S'$ :
$\begin{align*}\left( \Delta s \right)^2 = 25 c^2 \;\mathrm{min}^2 - c^2 \left(\Delta t \right)^2 \end{align*}$
$\left( \Delta s \right)^2$ must have the same value when evaluated in the two inertial frames, therefore
$\begin{align*}9 c^2 \;\mathrm{min}^2 = 25 c^2 \;\mathrm{min}^2 - c^2 \left(\Delta t \right)^2 \Rightarrow \Delta t = \boxed{...$
Therefore, answer (C) is correct.

Solution to 1996 Problem 50