A Trex its now believed could have run from no more then 10 to 45mph. Thats a big difference. I figure its 10 miles is not our 10 miles. It had huge feet and large body branches and roots would not have bothered it so much when running. A person would have to duck under branches and jump over roots. Plus avoid trees. In TRex time there were no paved road let alone dirt roads.
So I seriously doubt you could outrace even a at most 10mph TRex in their time. Today on a paved road maybe a slow TRex. 10 miles running would be hard on the lungs though. If TRex stamina is good I would bet on TRex.
Could I? No either time period. Hopefully TRex would choke on me.
So could you outrun a TRex.