$(10$ pts$)$ In the coordinate system S $,$ an observer measures a bright flash at $x_1=1200m,$ followed by a smaller flash $5$ ms later at $x_2=300m.$ Meanwhile, an observer in system S$\text{'}$ observes both flashes occurring at the same point $x^{\text{'}}.($refer to the figure below$)$

$($a$)(5$ pts$)$ Calculate the relative velocity $v$ of $S^{\text{'}}$ with respect to S and determine whether $S^{\text{'}}$ is moving in the $+x$ or $-x$ direction.

$($b$)(5$ pts$)$ Determine the time interval between the two flashes as measured by the observer in $S^{\text{'}}.$ State which flash occurs first.