Final answer:
To calculate the time to run 9 miles, we first find the athlete's speed from the given data of 8 miles in 15 minutes. The speed is 32 miles per hour. Using that speed, we find it will take approximately 16.875 minutes to run 9 miles.
Step-by-step explanation:
The student asks how long it would take an athlete to run 9 miles if the athlete ran 8 miles in 15 minutes. We will need to calculate the athlete's speed and then use it to estimate the time for 9 miles. First, we find the athlete's speed by dividing the distance by the time:
Speed = Distance ÷ Time
Speed = 8 miles ÷ 0.25 hours (since 15 minutes is a quarter of an hour)
Speed = 32 miles per hour
Next, we calculate the time to run 9 miles at that speed:
Time = Distance ÷ Speed
Time = 9 miles ÷ 32 miles per hour
Time = 0.28125 hours
Converting this time into minutes (by multiplying with 60) gives us:
Time = 0.28125 hours * 60 minutes/hour = 16.875 minutes
Therefore, it will take approximately 16.875 minutes for the athlete to run 9 miles at this rate.