The Trail of the Arrow -- Film Description:
"Although the film is no longer extant, there is some evidence of its approach. Trail of the Arrow weaves its story around a man by the name of Bob Battle who develops an aversion to women drivers when a woman motorist damages his fender. As a result of the accident, he challenges Shipman and her friend Marjorie Cole to a race. He makes a $1000 bet that the two women could not drive the Essex over a dangerous route in the Mojave Desert [...]. They immediately take him up on the wager."
-- Kay Armatage

Source:
Armatage, Kay. The Girl from God's Country: Nell Shipman and the Silent Cinema. Toronto: University of Toronto Press, 2003. (p. 123)