Explanation:

* Carbocation Stability: The rate-determining step in SN1 reactions is the formation of a carbocation intermediate. Tertiary carbocations are more stable than secondary or primary carbocations due to hyperconjugation.

* Leaving Group Ability: Bromide is a better leaving group than chloride. This is because bromide is a larger and less electronegative atom, making it easier to leave as an anion.

Therefore, tert-butyl bromide reacts faster in SN1 reactions because:

1. The tert-butyl group stabilizes the carbocation intermediate.

2. Bromide is a better leaving group than chloride.

Conclusion:

The combination of a more stable carbocation and a better leaving group makes tert-butyl bromide a more reactive substrate in SN1 reactions compared to tert-butyl chloride.