Which isomer of 1-bromo-4-tert-butylcyclohexane reacts faster when refluxed with potassium tert-butoxide? Draw the structure of the expected major product from the slower reacting compound.

Trans isomer

Explanation:

In this case, we will have an elimination reaction and due to the strong base (tert-butoxide) we will have an elimination reaction of second-order E2. Now, the leaving group is Br so we have to check the neighbors of this carbon that bonds the Br atom. If we have an E2 reaction we will need a special orientation for the hydrogens (180º antiperiplanar position) additionally, the Br atom needs to be in equatorial position (due to the steric hindrance). So, if Br is in equatorial position the hydrogens that can be removed are blue or red  (see figure 1). Because these ones have the special orientation that we need in an E2 reaction (180º). Now, the terbutyl group on carbon 4 also must have an equatorial position (due to the steric hindrance also). In this configuration, the terbutyl is pointing up and the Br is pointing down (green arrows). Therefore we will have opposite positions, so we will have a "Trans" configuration.

So, the isomer that will react faster is the trans isomer.

See figure 1.

I hope it helps!