Final answer:
At a consistent speed of 12 miles per hour, the student can run a total of 30 miles in 2 1/2 hours.
Step-by-step explanation:
If a student can run 6 miles in 1/2 hour, to find out how many miles they can run in 2 1/2 hours, we need to calculate the rate of speed and then use that to determine the total distance. The student's speed is calculated by dividing the distance (6 miles) by the time (1/2 hour):
Speed = Distance ÷ Time = 6 miles ÷ (1/2 hour) = 12 miles per hour.
Now, we multiply this speed by the total time to get the distance covered in 2 1/2 hours:
Distance = Speed × Time = 12 miles per hour × 2.5 hours = 30 miles.
Therefore, at the rate of 12 miles per hour, the student can run 30 miles in 2 1/2 hours.