You probably meant that the team ran [tex]2 \frac{2}{3} [/tex] laps around the track.
Length of running track = 34 miles.
Since the team ran [tex]2 \frac{2}{3} [/tex] times around the track, in order to find the total number of miles we multiply the length of track by [tex]2 \frac{2}{3} [/tex].
Therefore, total number of miles run by team will be equal to:
[tex]2 \frac{2}{3}*34 \\ \\
= \frac{8}{3}*34 \\ \\
= 91[/tex]
Rounding of to nearest mile, the team ran 91 miles around the track.