Is using the resultative complement 到 generally equivalent to saying "at the time this action was finished"?
Can 你走到车站的时候已经很晚了吗？ be translated as "By the time you reached the station were you already late?"
你跑到医务所的时候已经很晚了吗？ By the time you had run to the clinic, were you already late?
UPDATE: I noticed that different sources disagree on whether to call the 到 in the context you used it a complement of result. For example according to the Chinese Grammar Wiki it is not a complement of result (and it's also my feeling). The most common definition is that a complement of result implies that an action has attained the expected aim or result. However the Mandarin Essential Grammar Guide of the University of Yale lists this use case under complement of result. See below for more details.
In any case, regarding to your question
Is using the resultative complement 到 generally equivalent to saying "at the time this action was finished"?
In your examples the 到 doesn't refer to time but to the location where you arrived.
I would say this in not a complement of result.
In your examples the 到 is not a complement of result, but one to indicate direction, target or location. See Complements with "dao", "gei" and "zai"
The translation of your examples correct, but the reference to time doesn't come from 到, but from 的时候. 到 only refers to the location.
In case you actually are using a complement of result, the 到 will express that the outcome of the verb is achieved - what its result is.
For example
It emphasizes that the action has finished with a success.
Also see Result complements "dao" and "jian"
You can also express ability and possibility with these complements of result. For example:
The Mandarin Essential Grammar Guide of the University of Yale also has a section on the Complement of Result. In this they write (see http://comet.cls.yale.edu/mandarin/content/result/grammar/Result-9.htm):
dào到: implying that an action has attained the expected aim or result
- kàndào 看到 see
- tīngdào 听到 hear
- yùdào 遇到 run into
- jiēdào 接到 receive
- shōudào 收到 receive
- zhǎodào 找到 find
mǎidào 买到 succeed in buying
Example 1: zhǎodào找到 (zhǎo找to look for + dào到[attain the expected result]) find
Wǒ zhǎodào Lǐ Xiānsheng le. 我找到李先生了。 I have found Mr. Li.Example 2: mǎidào买到 (mǎi买to buy + dào到[attain the expected result]) succeed in buying Wǒ qùwǎn le. Méi yǒu mǎidào diànyǐng piào. 我去晚了。没有买到电影票。 I was late./ I got there late. [So,] I did not manage to get the movie tickets.
dào到: reach or arrive at (a place or a point of time)
- zǒudào 走到 walk to /until/up to
- pǎodào 跑到 run to /until/up to
- xuédào 学到 study until/up to,
- shuìdào 睡到 sleep until/up to
- mángdào 忙到 be busy until/up to
- kàndào 看到 read or watch until/up to
- tīngdào 听到 listen until/up to
Example 1: xuédào学到 (xué学to study + dào到 until/up to) study until/up to
Wǒmen xuédào Dì Bā Kè le. 我们学到第八课了。 We have studied up to Lesson 8 so far.Example 2: Zuótiān wǎnshang wǒmen xué Zhōngwén xuédào shíyī diǎn. 昨天晚上我们学中文学到十一点。 We studied Chinese until 11 o’clock last night.
In your case it refers to the fact that one reaches or arrives at a place. So the 到 on its own doesn't is not generally equivalent to saying "at the time this action was finished". The time reference comes from 的时候 (到的时候 = when (one) arrived)
Is using the resultative complement 到 generally equivalent to saying "at the time this action was finished"?
Yes, you can think of it that way, but not in the example you've provided.
If you want to use in that sense, 到 would be paired with 了, signifying "an end", or "in the past".
我到北京了。
Without the 了, "我到北京" would give no indication of time.
Think of 到 as a definitive destination identifier.
我明天到北京去！
到 here is identifying a set location for you to travel to.
As for your example sentence:
Can 你走到车站的时候已经很晚了吗？ be translated as "By the time you reached the station were you already late?"
You are correct that "晚" does mean "late", but moreso as a time of day. You can use 迟到 (Chí - "late, tardy, slow" Dào - "until", "arrive") to describe "being late for something", or "to arrive late".
你迟到车站了
Or, you can use 来得及 （Lái de jí- "in time for"）and 来不及 ("not in time for") to describe situations where you were your lateness actually caused you to miss something.
你来得及到火车站了， 让你刚好 (Gāng hǎo - "just", "happen to be")上火车了
You just made it to the train station on time, allowing you to just make your train
你来不及到火车站了，让你错过了火车
You arrived too late to the train station, so you missed your train!
For a general purpose word to describe "at this time this action was finished", you can use 完 (Wán - "complete"), or even 好.
我吃完了 - "I finished eating"
你完蛋了 - "You are finished (you are screwed)"
我做好功课了 - "I finished my homework"
