I know 趁着 means "to take advantage of a situation".
But I just came along two examples using 就 in the same sense. Are there any differences between them?
Chinese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Chinese language. It only takes a minute to sign up.Sign up to join this community
For the word 趁着：
It should be viewed in a whole structure, as in
趁着A, B。--> "While doing A/being in the situation of A, takes the opportunity to do B."
In addition, "趁着" will convey a meaning of being selfish (I am only caring about my advantage, yours is nothing, moods like this), which is definitely nothing good. So, in the example:
老师可以趁着学生是(这个)年龄再练习一下。 Will be barely OK, but then some may have negative feelings towards 老师.
For the word 就:
就A, B。 --> "According to the situation of A, do B."
In addition, "就A, B。" gives a mood of caring about others, or intending to say that "I am doing this for the sake of people who are affected by the situation A".
Of course, 就 could have many other meanings, but since I only want to focus on the difference between 趁着 and 就, I won't discuss here.
You know the correct meaning of 趁着 is "to take advantage of a situation", and maybe you also can translate it as "a situation gives you a chance to do something or to do something better".
The situation "mom is not at home" can be taken advantage of, so "it is good time for playing", we will have no more chance to play games after she comes back.
But "就" sometimes has different meaning. In your second sentence, it has same meaning as "趁着", but not in the first one.
"就" in the first sentence is probably better translated as "according to". It might have also different translations based on the whole context.
In my opinion "就" is better to be translated as "for (aimed to)" or "about".
You should make a speech for/about this situation
The sentence "老师可以趁着学生的年龄再练习一下。" is obviously wrong, you can not use "趁着" here.
First thing first, these two sentences have different meaning, and the latter is wrong. 老师可以就学生的年龄再练习一下。/老师可以趁着学生的年龄再练习一下。
You can't use 趁着 to objects such as students, stone, sexy girl. You can only use 趁着 to actions such as student practicing, stone thrown to you, sexy girl starving at you.
例如: 老师趁着学生在练习，去泡牛肉面吃。(correct) 老师趁着学生，去泡牛肉面吃。(incorrect, no meaning at all)
就 is a very versatile word that has many meanings. it can be used after objects and/or actions, and will have different meanings.
For example 就你。there are 2 totally different meanings to this simple sentence. 1, I will do anything to suit your need; (比例： 妹说：哥哥，我要。 哥说：好的，就你。) 2, in a negative way, questioning your ability. (比例： 哥说：我是最好学生。妹说：就你？)
While all of the answers above are sophisticated and rigorous. I will explain the usage of these two words in terms of their possible complementary usages in English.
就 can be used the same way as "with regards to/ regarding" For example, 就这个问题,我们再来谈谈 can be understood as "Regarding to this problem, let's talk about it again"
趁着 can be used the same way as "while" Borrowing the example from above, 老师趁着学生在练习，去泡牛肉面吃, can be understood as "While the students are studying/practicing, the teacher went to eat a bowl of beef noodle" (泡 means to soak in warm water, I didn't put that in the translation since it doesn't make sense in English to soak noodle.)
Hope that helps :)