1828, "artificial passage for water flowing from a fall or dam," from race (n.3) + way (n.). Meaning "automobile race course" is by 1936, from race (n.1).
Entries linking to raceway
race n.3
[strong current of water] c. 1300, more or less a particular sense of race (n.1), which then denoted any forward movement or swift running, from Old Norse ras in its sense of "a rushing of water." Via Norman French the word entered French as ras, which might have given English race its specialized meaning of "channel of a stream" (especially an artificial one, to a mill, etc.), which is recorded in English from 1560s.
way n.
Old English weg "road, path; course of travel; room, space, freedom of movement;" also, figuratively, "course of life" especially, in plural, "habits of life" as regards moral, ethical, or spiritual choices, from Proto-Germanic *wega- "course of travel, way" (source also of Old Saxon, Dutch weg, Old Norse vegr, Old Frisian wei, Old High German weg, German Weg, Gothic wigs "way"), from PIE root *wegh- "to go, move, transport in a vehicle."
From c. 1300 as "manner in which something occurs." Adverbial constructions attested since Middle English include this way "in this direction," that way "in that direction," both from late 15c.; out of the way "remote" (c. 1300). In the way "so placed as to impede" is from 1560s.
From the "course of life" sense comes way of life (c. 1600), get (or have) one's way (1590s), have it (one's) way (1709). From the "course of travel" sense comes the figurative go separate ways (1837); one way or (the) other (1550s); have it both ways (1847); and the figurative sense of come a long way (1922).
Adverbial phrase all the way "completely, to conclusion" is by 1915; sexual sense implied by 1924. Make way is from c. 1200. Ways and means "resources at a person's disposal" is attested from early 15c. (with mean (n.)). Way out "means of exit" is from 1926. Encouragement phrase way to go is short for that's the way to go.
race n.1
[act of running] late Old English, also rase, "a narrative, an account;" c. 1300, "an act of swift running, a hurried attack," also "a course of life or conduct, a swift current;" from Old Norse rās "a running, a rush (of water)," cognate with Old English ræs "a running, a rush, a leap, jump; a storming, an attack;" or else a survival of the Old English word with spelling and pronunciation influenced by the Old Norse noun and the verb. The Norse and Old English words are from Proto-Germanic *res- (source also of Middle Dutch rasen "to rave, rage," German rasen, Old English raesettan "to rage" (of fire)), from a variant form of PIE *ers- (1) "be in motion" (see err).
Originally a northern word, it became general in English c. 1550. Formerly used more broadly than now, of any course which has to be run, passed over, or gone through, such as the course of time or events or a life (c. 1300) or the track of a heavenly body across the sky (1580s). To rue (one's) race (15c.) was to repent the course one has taken.
Meaning "contest of speed involving two or more competitors; competitive trial in running, riding, etc." is from 1510s. For the sense of "artificial stream leading water to a mill, etc.," see race (n.3). Meaning "electoral contest for public office" is by 1827.