Translation:Faster! She is waiting for us.
Yeah "faster" would work if you imagine the people talking to each other are already running or driving a car to make it to the appointment. So it should be accepted but it shouldn't be the default answer. "Hurry up" should be the default.
I don't think 她在等着我们 is grammatically correct! Or is it? It should be either 在等 or 等着. Does anyone know the right answer?
You can have either or both. Apparently you can also add 呢 to the end to indicate continuing action.
I feel quickly or hurry is more natural in English. More people would tend to use it. Faster is very clunky. Are they walking? Are they driving? Then we would usually add a verb. Drive faster...walk faster.
Why is 在 and 着 around the verb 等 to indicate continuous action? Why not use only one? Like 她在等我们。 or 她等着我们
zai is an auxiliary verb while zhe indicates the continuous aspect. The use of zhe can sometimes be idiomatic and sometimes be classified as colloquial (source: allsetlearning, Chinese grammar wiki). According to this wiki some verbs use zhe more often than others, deng is on this list. So in Mandarin you would often say dengzhe. Ta dengzhe wo. Wo dengzhe ta. Ni dengzhe! (here they all mean to wait and keep waiting) Adding zai here means that she is waiting right now, the zhe to indicate that the waiting is ongoing. The sentences you mentioned are also correct, however the duo sentence, according to my Chinese friend, sounds better.
Ta deng women means he waits for us. Ta deng zhe women means he is waiting for us.
Well "zhe" emphasizes that the waiting is underway and ongoing. It's not used as often or as regularly as "-ing" is in English but means basically the same.
Waiting for and waiting on have two completely different meanings! Waiting on someone is what a waiter in a restaurant does. It means to serve someone.
"Waiting on" is certainly what a waiter does, but in reality "waiting on someone" is used all the time in the US. "Waiting on the bus" for "Waiting for the bus" and "Get on the airplane" for "Get in the airplane". "Take her to the airport" instead of "Bring her to the airport". "Y'all" and "Yous guys" for "You all" or "You". Even this course at least used to use "You Guys". But both are used extensively.
These are all regionalisms which should have no place in a language course. I have lived in California and Massachusetts but never heard anyone say "I am waiting on the bus" unless, of course" they are already on the bus and are waiting for others to arrive and join them on the bus. "Bring you to the airport" maybe correct in German but not in English. In English, bring and take are dependent on the direction from the speaker and the listener. I only heard foreigners say "I'll bring you to the airport" or "Could you bring me to the airport?"
Actually in some areas "bring" and "take" are used differently to how you know it. Irish people especially seem to use "bring" for most uses where others would use "take". But "take" is more standard and what the course should use by default even if it also accepts "bring" in some questions.