Difference between 趁着 and 就
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.