The easiest way to answer this question is to convert both times into minutes:
Roger:
2 and 2/3 hours
(60 minutes in an hour), so 2 x 60 + 2/3 x 60
= 120 + 40
= 160 minutes
Tina:
2 and 5/6 hours
2 x 60 + 5/6 x 60
= 120 + 50
= 170 minutes
As 160 is smaller than 170, Roger took less time to finish his test and therefore was the first one to be finished.