Is it farther or further?
"worthless stuff," mid-14c., junke "old cable or rope" (nautical), of uncertain origin, perhaps from Old French junc "rush, reed," also used figuratively as a type of something of little value, from Latin iuncus "rush, reed" (but OED finds "no evidence of connexion"). Nautical use extended to "old refuse from boats and ships" (1842), then to "old or discarded articles of any kind" (1884). Junk food is from 1971; junk art is from 1966; junk mail first attested 1954.
"Chinese sailing ship," 1610s, from Portuguese junco, from Malay jong "ship, large boat" (13c.), probably from Javanese djong.
1803, "to cut off in lumps," from junk (n.1). The meaning "to throw away as trash, to scrap" is from 1908. Related: Junked; junking.
New settlers (who should always be here as early in the spring as possible) begin to cut down the wood where they intend to erect their first house. As the trees are cut the branches are to be lopped off, and the trunks cut into lengths of 12 or 14 feet. This operation they call junking them; if they are not junked before fire is applied, they are much worse to junk afterwards. [letter dated Charlotte Town, Nov. 29, 1820, in "A Series of Letters Descriptive of Prince Edward Island," 1822]
[fr a British nautical term for old or weak rope or cable, found by 1485]