Halliday, Resnick & Walker — Relativity: Problem 48

48 In Fig. 37-9, observer S detects two flashes of light. A big flash occurs at $x_1 = 1000 \text{ m}$ and, slightly later, a small flash occurs at $x_2 = 480 \text{ m}$. The time interval between the flashes is $\Delta t = t_2 - t_1$. What is the smallest value of $\Delta t$ for which observer $S'$ will determine that the two flashes occur at the same $x'$ coordinate?