OK,

The driver need to cover 1 mile in one minute.

Over the first 30 seconds, he's averaged 30 mph, (which works out at 0.5 miles per minute) Therefore he's covered 0.25 of a mile.

He needs to cover 0.75 miles within the next 30 seconds.

So he needs to travel at 1.5 miles per minute, which works out at 90 mph.

For some reason, (whilst it seems logical) I've got a feeling that my answer is wrong.

Ed