ai) Madison plans to walk and run a total of \( 1 \frac{4}{5} \mathrm{mi} \) on 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. Let \( r \) be the distance in miles that Madison needs to run. Describe the situation with an equation.

To find the distance Madison needs to run, we can set up the equation as follows: \[ r = 1 \frac{4}{5} - \frac{2}{5} \] This equation states that the distance Madison needs to run (\( r \)) is equal to the total distance (\( 1 \frac{4}{5} \) miles) minus the distance she has already walked (\( \frac{2}{5} \) miles). Now, let's convert \( 1 \frac{4}{5} \) miles to an improper fraction to make the calculation easier: \[ 1 \frac{4}{5} = \frac{9}{5} \] Now our equation looks like this: \[ r = \frac{9}{5} - \frac{2}{5} \] This will help Madison figure out how far she needs to run to complete her workout!