Ashi Girl

Hayakawa Yui is a 16-year-old girl whose only strong point is her ability to run fast. When her reclusive but genius younger brother invents a time machine, she accidentally gets sent to the Warring States era and meets the young lord of the Hagi clan, Hagi Tadakiyo, and falls in love with him. Upon returning back to her modern time, she discovers from her high-school teacher that the Hagi clan are doomed to be wiped out in history. Desperate to save this young lord, she finds her way back to the Warring States era, and so her adventure there begins.
(Source: MDL)
~~ Adapted from the manga "Ashi Girl" (アシガール) by Morimoto Kozueko (森本梢).