Taking a break between school and university is worthy of their time.
OK so here it would be better to write:
And so why, in this situation, is it better to write worth rather than worthy (of)?
Use worth when you want to evaluate a thing, person, or action:
This is particularly useful when you want to evaluate claims in IELTS Task 2 writing.
Use worthy (of) when you want to say that a thing, person or action deserves attention, effort, or respect. The key word here is deserve:
Note that worthy (of) is now considered quite old fashioned. These days it is used more often to refer to people rather than things. The last two examples would now more likely be written:
Unfortunately there are some grammar and collocation issues relating to the word worth. Lucky for you, these are described with examples in a previous post.