Final answer:
Based on the runner's performance of maintaining a consistent pace, completing 2.6 miles in 20 minutes and 10.4 miles after 1 hour 20 minutes, we conjecture an average speed of 7.8 miles per hour. To complete the 26.22-mile marathon, it would take approximately 3 hours and 42 minutes.
Step-by-step explanation:
To conjecture the runner's average speed in miles per hour, we can use the information provided. The runner completes 2.6 miles in 20 minutes, and after 1 hour and 20 minutes, the runner has completed 10.4 miles.
First, we convert the time to hours to maintain consistent units:
20 minutes is ⅓ of an hour.
1 hour 20 minutes is 1+⅓ hours, which equals ⅛ hours.
To find the runner's average speed in miles per hour, we use the formula:
Average speed = Total distance / Total time
For the first 2.6 miles:
Average speed = 2.6 miles / ⅓ hour = 7.8 mph
\For the next 7.8 miles (10.4 total miles - 2.6 initial miles):
Average speed = 7.8 miles / 1 hour = 7.8 mph
Thus, we can conjecture that the runner's average speed is consistent at 7.8 mph. Now to estimate the total time to complete the marathon, which is 26.22 miles long, we can use this average speed:
Total time = Total distance / Average speed
Total time = 26.22 miles / 7.8 mph ≈ 3.36 hours, which is about 3 hours and 22 minutes.
We must consider the initial 20 minutes in our final time calculation, so the total expected time is 3 hours 42 minutes.