Green’s Dictionary of Slang

satisfactorily.

1918		E.G. Dodd diary 15 Aug. 🌐 Came up the line this morning and found Aster running at 6k. Jim Page tells me that Aster [i.e. an engine] is going Jake. [Ibid.] 26 Sept. Changed the field magnets on the magneto and she kicked off Jake.
1934		(con. 1920s) J.T. Farrell Young Manhood in Studs Lonigan (1936) 283: They’ll fix me up jake with a nice new Ford and something to spare.
1940		S. Sterling ‘Ten Carats of Lead’ in Black Mask Stories (2010) 223/1: Me an’ Tom MacReady always got along jake.
1949		J.T. Farrell ‘Slouch’ in Amer. Dream Girl (1950) 101: Everything went along jake for a while.