Can You Solve This Speeding Problem?

Tom Rigg of Brutus, Michigan, writes:

Marilyn: I have a bet with my friend. Here's the problem: Say you have a one-mile straight track. For the first 1/2 mile, you travel at exactly 30 mph. Discounting acceleration time, how fast do you have to travel the last 1/2 mile to average 60 mph over the course? My friend says 90 mph, and I say it can't be done.

At 30 mph, it takes one minute to travel the first 1/2 mile. At 60 mph, it takes one minute to travel the full track. But as you used up that one minute in first 1/2 mile, there is no time left for you to travel the last 1/2 mile fast enough. Who's right on this one?

Marilyn responds:

You're right, Tom. It can't be done.