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The train is running at a speed of 65 kms per hour. The train is running at a speed of 65 kms an hour. Which one is grammatically correct?

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I would not go so far as to say either are incorrect, but I would say that per is the more accurate phrasing. Why? Because in the context of this statement per means "for each", and that is precisely what is meant: the train travels 65 km for each hour. an has no such meaning.

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    M-W says it has: << an preposition .. Definition of an (Entry 2 of 9): (see a entry 3 sense 2): {Definition of a : in, to, or for each – twice a week, [three times an hour]} sixty miles an hour. Feb 20 '20 at 17:58
  • @EdwinAshworth: I saw that, but still feel per is more accurate. Do you disagree?
    – Seamus
    Feb 20 '20 at 18:04
  • These Google 4-grams show that 'sixty miles an hour' is (and has been for a long time) roughly twice as accurate as 'sixty miles per hour' if the standard used is 'what people actually say'. ELU deals with what people actually say and find acceptable, not in the first instance what some feel better reflects the history of words' meanings. Feb 20 '20 at 19:03
  • '[I]n the context of this statement per means "for each"; an has no such meaning' where a respected dictionary reads 'an preposition: in, to, or for each – twice a week, [three times an hour]} sixty miles an hour' seems the source of the obfuscation here. I didn't answer because there was (a) a previous identical question and (b) no reasonable research in the question. There's none in your answer, either. Feb 25 '20 at 11:52

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