"To book" used as "to run"

Is it correct to use the verb to book with the meaning of to run? I heard this usage in situations like:

The dog ran out and I booked it after him.

or

I was booking it down the hill.

I couldn't find any meaning similar to this in the Merriam-Webster Dictionary or others.

Book here is used informally as a verb meaning hurry or move quickly.

He didn't watch the show because he had to book it to school.

Urban dictionary has a good description of this usage.

It is slang, but it means to leave rapidly or run quickly.

Without proper proof, I believe the origin to be something akin to "enter the record books". Or, per Urban Dictionary it may be related to leaving a party quickly to go and study (hit the books).