The compound adjective 'three-minute' is a transparent modern English formation, combining a cardinal number with a standard unit of temporal measurement. The word 'three' descends from the Proto-Indo-European root trei-, which is the source for the number across many Indo-European languages, signifying a fundamental quantitative concept. 'Minute' entered English via medieval Latin and French, its meaning shifting from the literal sense of 'a small part' (from minuere, 'to make smaller') to specifically denote a sixtieth of an hour, a small division of time. The hyphenated compound logically and directly denotes a duration measurable as three of these specific temporal units.

Structure: three (quantity) + minute (time unit) - three: From Old English þrīe, þrēo, of Proto-Germanic origin; related to Latin trēs, Greek treis. Functions as a cardinal number. - minute: From Old French minute, from Latin minūta ('small', 'minute' as a unit of time), feminine of minūtus ('small'), past participle of minuere ('to lessen'). Functions as a noun denoting a unit of time.