Final answer:
To run 5 miles in less than 60 minutes, Peggy's rate should be faster than 1 mile per 12 minutes, which is represented by the inequality 1 mile < 12 minutes.
Step-by-step explanation:
Peggy wishes to run 5 miles in less than 60 minutes, so we must determine the minimum rate at which she needs to run. This transaction of distance over time is represented with a rate or speed. Since we're discussing an inequality that represents what her rate should be, we use the notion that time is less than 60 minutes. If she runs at a constant rate, Peggy needs to run each mile in less than one-fifth of the time allotted for 5 miles to ensure she finishes on time.
The calculation is simple: 60 minutes / 5 miles equals 12 minutes per mile as the target pace. Therefore, Peggy's running rate should be faster than 1 mile per 12 minutes to complete her goal. This relationship can be represented by the inequality 1 mile < 12 minutes. This indicates that for every mile Peggy runs, the time taken should be less than 12 minutes to meet her goal of running 5 miles in under an hour.