[frankenstein18]

why do tertiary alkyl halides prefer Sn1 over E1 even though they can undergo both?

[beardy]

Tertiary alkyl halides can also undergo E2 with a strong base. Tertiary alkyl halide doesn't necessarily prefer substitution or elimination. Sometimes you get a mixture. You must consider other reagents to determine which pathway is more likely.

How to avoid mixes:

 sn1: weakly basic nucleophiles (water, alcohol)
 e1: non-nucleophilic bases: choose an acid with a weakly nucleophilic counterion [H2SO4, TsOH, or H3PO4], and heat.