Problem 1.357

The space-time diagram of Fig. 1.93 shows three events $A$, $B,$ and $C$ which occurred on the $x$ axis of some inertial reference frame. Find: (a) the time interval between the events $A$ and $B$ in the reference frame where the two events occurred at the same point; (b) the distance between the points at which the events $A$ and $C$ occurred in the reference frame where these two events are simultaneous.