A firecracker explodes in reference frame S at t $=1\mathrm{.}0$ s$.$ A second firecracker explodes at the same position at t $=3\mathrm{.}0$ s$.$ In reference frame S$\text{'},$ which moves in the x$-$direction at speed v$,$ the first explosion is detected at x$\text{'}=4\mathrm{.}0$ m and the second at x$\text{'}=-4\mathrm{.}0$m$.$

a$)$ What is the speed of frame S$\text{'}$ relative to frame S$?$

b$)$ What is the position of the two explosions in frame S$?$