It's a frequently asked question in English study forums in China (recently here). How do you say "第几" in English? When A asks B, "这是你第几次来纽约?" (literally, "This is which time you come to New York?"), B may answer "第二次" ("The second time"). A more natural English question may be, "How many times have you come to New York?", "Twice", or "How many times did you come to New York before?", "Only once (before)".
The awkward "which time" is a literal equivalent of "第几次" as in "Which time is it you come to New York?" The English "time" is one word for both the time you use a clock to keep track of and the ordinal count of repetition of you doing something, which is a measure word. Other languages may use two words for these meanings (时间, Zeit, tiempo, temps, tempo vs. 次, Mal, vez, fois, volta, respectively). The reason "which time" sounds unnatural may be related to this particular polysemy (one word having multiple meanings) of English "time".
Here are more challenging ones, "第几个", "第几件", and "第几本", as in "老师要我们读John Smith的ABC系列的所有三本书，你在读第几本?" ("The teacher wants us to read John Smith's all three books in the ABC series. Which book are you reading now?") But "Which book are you reading?" is not a good translation because the answer may well be "I'm reading his Book Title". The question in Chinese actually demands the answer "I'm reading his first|second|third book". English "which" properly matches "哪一(本)". It does not specifically ask the ordinal number as the Chinese "第几(本)". The fact that these Chinese question words are more challenging is probably because "个" and "本" have no measure word equivalents in English, and although "件" may be "piece", "Which piece ...?" does not specifically demand an answer of the ordinal number in the series.
A little follow-up. A Chinese reader says "So English is deficient?" My answer is that every language may have stronger expressive power than another in one case, but less in another. In this case, Chinese wins. In the case of subjunctive mood, Chinese loses (you have to guess whether "如果我有1000块钱" is the counter-factual "if I had 1000 dollars", although "如果我是你" is definitely "if I were you"). In the textbook case of ambiguous English sentence "He hit the man with a stick", Chinese wins because you can't make up an ambiguous sentence in Chinese. And the list goes on.
(This posting has a follow-up.)