Nancy's average weekly mileage has increased by 20%.
To find the percentage increase in Nancy's average weekly mileage, we can use the following formula:
![[ \text{Percentage increase} = \frac{\text{New average} - \text{Old average}}{\text{Old average}} * 100% ]](https://img.qammunity.org/2024/formulas/mathematics/college/4ujx8ybjicx1wjlugw9kmkdukq6di015b6.png)
Given that Nancy averaged 5 miles per week last month and 6 miles per week this month, we can substitute these values into the formula:
![[ \text{Percentage increase} = (6 - 5)/(5) * 100% ]](https://img.qammunity.org/2024/formulas/mathematics/college/953qtbm3xie8aqvbbslv78kz5l61rei9t4.png)
![[ \text{Percentage increase} = (1)/(5) * 100% ]](https://img.qammunity.org/2024/formulas/mathematics/college/gf90nanhb1y1a1tql31b30nntbmncbx01x.png)
![[ \text{Percentage increase} = 20% ]](https://img.qammunity.org/2024/formulas/mathematics/college/q8br8mc5nyfj0o8sp7ogfsut237wc8o8bv.png)
Therefore, Nancy's average weekly mileage has increased by 20%.