Minor was a four-year letterman for the Florida State Seminoles where he started 33 of the 43 games in which he played during his career, including 30 starts over his final three years. He finished his career with 3,218 yards rushing and 28 touchdowns on 664 attempts, while also catching 106 passes for 831 yards and three scores and is the school's third all-time leading rusher, trailing only Warrick Dunn (3,959) and Greg Allen (3,769). He led team in rushing all four years and was a second-team All-Atlantic Coast Conference selection as a senior when he rushed for a career-high 923 yards and five touchdowns on 181 carries, and tallied a career-best 42 receptions for 333 yards. He played in the Senior Bowl following his senior season. Coincidentally, Travis Minor and Warrick Dunn also attended the same high school. (Catholic High, Baton Rouge) He was a sports management major.
Minor was drafted in the third round (85th overall) by the Miami Dolphins in the 2001 NFL Draft. The Rams signed Minor on March 7, 2007. He was the Rams starting back for most part of the 2007 season in which he gained a career high 4 TD in a season and gained an aveage of 1.4 yards per carry.
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