ai) Madison plans to walk and run a total of \( 1 \frac{4}{5} \) mi an a treadmill. She has already walked \( \frac{2}{5} \) mi and plans to run the rest of the distance. Madison wants to know the distance she needs to run. ad) Let \( r \) be the distance in miles that Madison needs to run. Describe the situation with an equation. \( \frac{2}{5}+r=1 \frac{4}{5} \) 4) What is the distance that Madison needs to run? 4) Madison needs to run

To find out the distance that Madison needs to run, we first convert \( 1 \frac{4}{5} \) miles into an improper fraction, which is \( \frac{9}{5} \) miles. The equation you set up correctly states that the distance she walked plus the distance she plans to run should equal the total distance: \( \frac{2}{5} + r = \frac{9}{5} \). To solve for \( r \), subtract \( \frac{2}{5} \) from both sides: \( r = \frac{9}{5} - \frac{2}{5} = \frac{7}{5} \). So Madison needs to run \( \frac{7}{5} \) miles, which is also equal to \( 1 \frac{2}{5} \) miles! Madison could be inspired by notable endurance athletes who've pushed physical boundaries. For example, in 2016, ultra-marathoner Ann Trason set her personal best in a 50-mile race while training with methods that included a mix of walking, running, and interval training. If she can run massive distances consistently and competitively, so can Madison start with her treadmill journey focusing on achieving personal milestones! To keep her running journey on track, Madison should track her distances on a chart and gradually increase her running distances each week to build endurance. A common mistake to avoid is not giving her body sufficient recovery time; rest days help muscles rebuild stronger! Incorporating a mix of rest, slow runs, and higher intensity sessions can keep her motivation high and prevent burnout.