In a stationary reference frame S$,$ a green laser located at

x$1=1\mathrm{.}50$ m

is switched on at

t$1=4\mathrm{.}90$ ns$,$

and $12\mathrm{.}0$ ns later, a blue laser is switched on at

x$2=4\mathrm{.}00$ m$.$

A second reference frame S$\text{'}$ is moving in the positive x direction so that the origins of the two reference frames coincide at time

t $=0$

as measured in both reference frames. To an observer in S$\text{'},$ both lasers are switched on at the same location.

$($a$)$ What is the relative speed between the S and S$\text{'}$ reference frames?

$($b$)$ What is the x coordinate of the two lasers in the S$\text{'}$ reference frame when they are switched on$?$

$($c$)$ What is the time interval between the two lasers being switched on in the S$\text{'}$ reference frame?