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Phrase(s): run down to someone or something
to come or go down to someone or something, rapidly. • Sally ran down the slope to Bob, who stood waiting for her with outstretched arms. • I ran down to the well to get some water for Ed, who had the hiccups., Phrase(s): run down to some place
to travel to a place. (By running or any other means.) • I have to run down to the store and get some bread. • I want to run down to the bank, but my car is out of gas.
McGrawhill's American Idioms And Phrasal Verbs