I studied Russian in college, many years ago. I have been pleasantly surprised at how much is coming back to me. One thing I remember clearly is that we always said на метро. I still have my textbook, and I checked to be sure. Has this changed over the years, or do Russians sometimes (or in some places) still say на метро?
I have never been to Moscow (how I wsh I could go there some day!) but I believe it has only one subway system, the Metro. However, it would have many taxis. So Jenny could be on THE (only) subway or in A taxi (one of many).. In the case of "a book" vs "the book," the first would mean any book or an unspecified book, while the second would mean a book mentioned earlier in the conversation or known to speaker and/or listener. Here the context determines which is used. Since Duo's sentences do not supply context, either one is usually accepted in these cases.
Is Jenny on the subway or in the taxi? It was accepted, and I personally think it's the most correct way to say it in English.