Final answer:
Sarah will have run a total of approximately 37.15 miles after 10 weeks.
Step-by-step explanation:
To find the total number of miles Sarah will have run after 10 weeks, we can use the formula for compound interest:
Total distance = initial distance * (1 + rate of increase)^number of weeks
Using the given information:
- Initial distance = 6 miles
- Rate of increase = 20% or 0.2
- Number of weeks = 10
Plugging these values into the formula:
Total distance = 6 miles * (1 + 0.2)^10
Simplifying:
Total distance = 6 miles * 1.2^10
Total distance = 6 miles * 6.1917364224
Total distance = 37.1504185344 miles
Therefore, Sarah will have run a total of approximately 37.15 miles after 10 weeks.