The problem with the translation of this sentence into english is, that the preverb "el-" gives the meaning of completed action. The act of traveling is not fullfilled yet but the result of it is put into the focus.
For me as a native German it is easy/ier to understand, because in German we also have these preverbs and differ between "utazni = reisen" and "elutazni = verreisen".
So sometimes it seems to me, that Hungarian is much easier to learn for a German speaking than for an English speaking person. ;-)
That could be true. :) And you are also very much used to the beauties of conjugation. Also, German was the official language in Hungary for a long time. So it had a great effect on the language. Also, when the Hungarian language was reinvented, many new words were created by literal translation of German words. So, really, it should be like child's play to you. :)