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 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:
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They are only in their second year, so they can't Apparate.
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Keep to the constraints of the problem. The broom can't be snapped in half.
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Bonus points for spotting a Harry Potter mistake in the question.
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Have Harry jump onto the broom and fly half the distance, leaving Ron huffing and puffing and wheezing behind. Harry gets off the broom and starts walking. Ron finally gets to the halfway mark, sees the broom and sits on it. The broom carries him to the station, which Harry is just reaching at 1 8 . 7 5 minutes.
Quantitatively:
When Ron gets to the broom at halfway, 1 2 . 5 minutes have passed. He then flies the rest of the way in 6 . 2 5 minutes. He thus gets to the station in 1 2 . 5 + 6 . 2 5 = 1 8 . 7 5 minutes. By symmetry, Harry gets there at the same time. They are 1 5 seconds early!
They congratulate themselves on their success and run at the barrier...
Continued in Harry Potter and the Chamber of Secrets .