How long can you keep up this pace for? or For how long can you keep up this pace?
At what time does your train leave? or What time does your train leave at?
I've heard native English speakers saying it both ways but from a grammar standpoint which is the correct one?
Thanks
Both are correct and have a long history in the English language. The poet John Dryden is said to have first questioned ending a clause with a preposition, and ever since it has at times been frowned upon. ("Frowned upon!") Some find it inelegant. But I always take Fowler as my unerring authority in everything English: " 'One of the most persistent myths about prepositions in English is that they properly belong before the word or words they govern and should not be placed at the end of a clause or sentence' " (quoted from Wikipedia).
I think, however, that when the verb and the final preposition don't follow in direct succession, as in your example ("How long can you keep up this pace for?"), the construction becomes somewhat awkward; in that case, "For how long can you keep up this pace?" sounds better.
How long can you keep up this pace for?
What time does your train leave at?
Or you can just say, "what time does your train leave?" And "how long can you keep up this pace?"
These sound more fluent.