Well, well, well, we are in trouble

Harry Potter and Ron Weasley need to get to Paddington station as quickly as possible since the Hogwarts Express leaves from platform $9 \frac{3}{4}$ in 19 minutes. If they were to both run, they would get to the station in only 25 minutes.

However, by a stroke of luck, one of them has a broom, which, alas, can only carry one person at a time. The broom can fly twice as fast as one of the boys can run. But this is an old, cheap broom: it cannot fly by itself. Either Harry or Ron must sit on the broom, and the other must run.

Can they catch the train?

Details and Assumptions:

• They are only in their second year, so they can't Apparate.

• Keep to the constraints of the problem. The broom can't be snapped in half.

• Bonus points for spotting a Harry Potter mistake in the question.