Answer
2-Bromopropane will react faster by the $S_N1$ mechanism.
Work Step by Step
We know that the structure which forms a more stable carbocation will react faster by the $S_N1$ mechanism. In the given pair, 2-Bromopropane will form a $2^\circ$ carbocation, which is more stable. So, 2-Bromopropane will react faster by the $S_N1$ mechanism.