Prove that if 2000 m is run in 4:50, then one continuous mile is run under 4:00.
I was thinking -- yeah, this follows easily from the other question, where I asked that if 2 miles are run in 7:59, then one mile must be run under 4:00.
But then I read that paper that Arturo provided a link to, and as 2000 m is not an integer multiple of 1609.344 m (1 mile). Now I am not in fact sure whether this is indeed true. The author of the paper, R. P. Boas, uses the universal chord theorem for cases where the total distance is an integer multiple of the distance in question, but says that for non-integer cases. It is not necessarily the case that a distance less than the total is ever covered in
(average speed)*(that distance) or better.
Can there be shed some light on this?
(This is a follow-up from my last question, but I believe it is somewhat more difficult.)