I don't quite get this one--I thought that "acabar de" was used to signify something that was just done. As in "acabar de comer," to have just finished eating. Using it in the future tense confuses me!
Think of it in this context: "By the time Juan arrives, we are going to finish eating."
I think this may also relate to the difference between terminar and acabar; my impression is that while terminar says that something is finished; acabar says that something has just finished. So if you're using acabar to translate my sentence in quotes, you're saying that you think Juan is going to arrive just after your meal is over. If you use terminar, it would be more open-ended -- you might finish long before he arrives. (Which would be sort of an odd thing to say, given that people eat on a fairly regular basis.)
I would say that to 'finish up' is colloquial (slang). it also tends to be used as a command/when you need someone to hurry up i.e. 'finish up, we need to get moving' or 'finish up or we won't make the movie'.
See how using this in the phrases above has created informal/slang/idiomatic sentences. I don't think it suits the context of the sentence given or duolingo.
Personally I might say 'finish up' to someone directly while they were eating without including the word 'eating' (this could be considered rude) or towards myself 'i'm just going to finish up, then i'll be right with you'
However, I do not feel that the phrase 'finish up eating' is strictly, grammatically wrong though
The phrasal future (ir + infinitive) is used for near future, definite events. (If you're including a temporal word like "mañana", you can even get away with just using the simple present tense.)
If you're discussing something more speculative or long-term, you'd be somewhat more likely to use the actual future tense.
"We are going to finish to eat" sounds wrong. I couldn't explain why it sounds wrong, so I searched online for you. There are many sites that explain the "going to" future in English, but they don't answer your question. I'd pay serious money for a book that explained all English grammar! I don't think it exists. Have no fear, I think i did find your answer.
Some verbs take a gerund while others take an infinitive.
http://www.englishpage.com/gerunds/part_1.htm scroll to number 5, hit the link, and you get this list: http://www.englishpage.com/gerunds/gerund_list.htm
This list isn't using the "going" future, but you can use those verbs with the "going" future. These verbs take a gerund either way.
I also want to note that the word Gerund does not mean Gerundio. Gerundio means present participle. The english word Gerund is an -ing word used as a noun, which of course doesn't exist in Spanish. Some people inaccurately call any -ing word a gerund. Being aware of this common mistake can help prevent confusion when reading free grammar sites online.
Second note: some of these don't fit well into the "going" future. Particularly the ones that start with "can't." If anyone finds a better list, please share it!
Nosotros acabamos de comer = We just ate. We just got done eating. We just finished eating.
Nosotros vamos a acabar de comer. This construction seems iffy, even in Spanish. It could mean "We will have just eaten (, so that would be a perfect time to drink a brandy) ." I think I would say "Acabaremos de comer."
First up, as a native english speaker I cannot think of any context in which you can say 'will to' when 'will' and 'to' have this meaning. Think of this as a verb/preposition rule. In contrast, 'going to' is a very common phrasing.
Additionally in english, the phrase 'to eat' would suggest that you have not started eating. I.e. you can use the future phrasal to say 'today we are going to eat' (hoy vamos a comer)
However, if the near future action is to 'finish' another action, then the future tense will reflect that you are performing that action currently. (I.e. you are eating)
Consequently: Vamos a acabar de comer becomes 'we are going to finish eating' or 'we will finish eating'
Let me know if you need any more info on this