Answers (E) must be wrong because the relationship between $\Delta t_1$ and $\Delta t_2$ cannot depend on inertial frame $S_3$ . Answers (C) and (D) must be wrong. This can be seen from the case when inertial frame $S_2$ and $S_3$ are moving with equal speeds in opposite directions, relative to th inertial frame $S_1$ . Then the average lifetime in them must be equal, which it is not according to answer (C) or answer (D). To select between answers (A) and (B), recall that ``moving clocks run slow" and that $\gamma = 1/\sqrt{1 - v^2/c^2}$ is the factor that relates time differences in two inertial frames. This implies that answer (B) is correct.

Solution to 1992 Problem 38