Answer
Firecracker 2 exploded at $~~t_2 = 2.0\times 10^{-6}~s$
Work Step by Step
We can find the time $t$ it took for the light from firecracker 1 to reach Bjorn:
$t = \frac{d}{c} = \frac{600~m}{3.0\times 10^8~m/s} = 2.0\times 10^{-6}~s$
We can find the time firecracker 1 exploded:
$t_1 = (3.0\times 10^{-6}~s) -( 2.0\times 10^{-6}~s)$
$t_1 = 1.0\times 10^{-6}~s$
We can find the time $t$ it took for the light from firecracker 2 to reach Bjorn:
$t = \frac{d}{c} = \frac{300~m}{3.0\times 10^8~m/s} = 1.0\times 10^{-6}~s$
We can find the time firecracker 2 exploded:
$t_2 = (3.0\times 10^{-6}~s) -(1.0\times 10^{-6}~s)$
$t_2 = 2.0\times 10^{-6}~s$
Firecracker 2 exploded at $~~t_2 = 2.0\times 10^{-6}~s$
