Taking a break between school and university is worthy of their time.

OK so here it would be better to write:

• Taking a break between school and university is worth doing.

And so why, in this situation, is it better to write worth rather than worthy (of)?

Worth

Use worth when you want to evaluate a thing, person, or action:

• Exercise is worth doing. (positive evaluation of ‘exercise’)
• Smoking isn’t worth it! (negative evaluation of ‘smoking’)
• That guy’s worth a million dollars. (positive financial evaluation)

This is particularly useful when you want to evaluate claims in IELTS Task 2 writing.

Worthy (of)

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:

• He’s not worthy. (= He doesn’t deserve our respect.)
• Two incidents are worthy of mention here. (= Two incidents deserve our attention.)
• The poem is worthy of deep reflection. (= The poem deserves our effort.)

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:

• Two incidents are worth mentioning here.
• The poem is worth reflecting upon.

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.