If you are indeed responsible for the delay, then it is obviously correct to say so.
If they are in fact waiting there, it is perfectly correct to say so.
It is correct to say "On the train" when you are inside it. either one will work This is also known as being 'on board' the train.
get on a train can be translated as:einen Zug besteigenIn einen Zug einsteigeneinen Zug nehmen
電車 (densha)/ 列車 (resha)/ 汽車 (kisha)
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