'Let's vacation together' seems to be a weird literal translation. I'm guessing 같이 여행하자 is 'Let's go on vacation together'
I think in some forms of english, vacation is used as a verb as well as a noun
I think the problem there is that vacation doesn't necessarily mean travel.
여행 is a trip or a journey, so really it should be something like "Let's go a trip together" or "Let's travel together"
It didn't accept "let's go on holiday together"?! The word vacation doesn't even exist in british english. Come on.
"Let's take a trip together" also seems an equivalent translation, but this was not accepted.
여행 is used here both as to vacation, a vacation, and travel. It makes sense. Cause 방학 means school vacation, not necessarily vacation in general, so 여행 is used for vacation.
"Let's holiday together" I have heard, BUT "Let's vacation together", not from a native speaker...
"let's vacation together" this is not natural english. it's much better to say "let's go on holiday together" or "let's travel together"