How to use 得 without single-character verbs (e.g. 我旅行得很快)? I've been taught that ‘得’ can be used in situations such as, “我打篮球打得很好”, to describe the "degree" that the action has. But I've also been told that ‘得’ only works with single character verbs-- so rather than saying, “我游泳得很快”, I would say, “我游得很快”, instead.

This is all fine and well for verbs like ‘游泳’ which can be replaced by ‘游’ but for other verbs whose individual characters don't mean anything on their own, I'm not sure what to do.

I am unable to say, "I travel very fast," because I can't say “我旅行得很快”. What is the solution to this?
I would say that "A得B"(述语+补语) form does not add constraint on the number of characters of either A or B. But if encountering a choice between "学得快" and "学习得快" in oral language, most native speakers would select the former one since it's shorter, although both of them are correct from the view of grammar.

For the case of "旅行得很快", I don't think it's incorrect in grammar. If you have a reasonable context, it can also appear in oral language, although people would prefer saying "旅游" or "玩" to "旅行" (which sound too formal, like written language). Since people would not often talking about how fast their travelling is, many people may think this odd.

Moreover, although "学" and "学习" can be used as both noun and verb. In most cases orally, "学" uses as verb and "学习" as noun.

Some more examples of "A得B" form with more than one character in A:


这个项目计划得很周密。

This project plans thoroughly.
他高兴得眼泪都流出来了。

He is happy into tears.
这首歌要好听得多。

This song is much better.