Final answer:
An athlete will take approximately 16 minutes and 52.5 seconds for the athlete to run 9 miles at this rate.
Step-by-step explanation:
To find out how long it would take an athlete to run 9 miles given they ran 8 miles in 15 minutes, we need to calculate their running rate and then use that rate to determine the time it would take to cover 9 miles.
The athlete's running rate can be calculated by dividing the distance (8 miles) by the time (15 minutes). In terms of hours, since there are 60 minutes in an hour, the athlete ran 8 miles in ⅓ hours (or 0.25 hours).
Therefore, the athlete's speed is 32 miles per hour (8 miles ÷ 0.25 hours).
Now, to run 9 miles at a speed of 32 miles per hour, we calculate the time as follows:
Time = Distance ÷ Speed
Time = 9 miles ÷ 32 miles per hour
= 0.28125 hours.
To convert this back into minutes, we multiply by 60 giving us :
Time = 0.28125 hours × 60 minutes/hour
= 16.875 minutes.
Therefore, it will take approximately 16 minutes and 52.5 seconds for the athlete to run 9 miles at this rate.