Solution to 1992 Problem 38

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.

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