There was not a single extra Professor invited for this contest. That's why only the Headmistress and the mentor were accompanying the students to the venue.
It takes about six hours to reach there and since they have left early in the morning, they will reach the tower by afternoon.
The carriage was being pulled by four horses and one driver was leading the carriage toward the destination.
The Runebound academy was situated near the northern region of the nation—beyond the border were wastelands, which appears in stark contrast to the greenery in this part of the nation.
The Mage Tower is located in the east of the academy—that's why it takes so much time to travel between the capital and the Tower since the Capital is in the south of the Academy.
While the academy and the tower are on the border, the Capital is nearly at the heart of the nation, but since there is only one route to travel between the three landmarks, people generally use Teleportation—if it is an emergency.