The Impossible Hour is a concentrated study of Ole Ritter's attempt in Mexico City in 1974 to set a new record for the hour - described in the film as "the noblest, most difficult record that can be set on a bicycle". A brief retrospective in black and white sets the historical framework, with shots of Ritter and Eddy Merckx' successful record attempts in 1968 and 1972 respectively, and a few words about former record holders such as Fausto Coppi.The film follows Ritter's three record attempts chronologically, which, accompanied by a Mexican marching band on the bandstand, all fail.

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