Question

rafael runs each lap in 7 minutes. he will run at least 12 laps today. what are the possible numbers of minutes he will run today? use t for the number of minutes he will run today. write your answer as an inequality solved for t.

Explanation:

Step1: Define the relationship

Each lap takes 7 minutes, and he runs at least 12 laps. Let \( t \) be the total minutes. The total time \( t \) is the number of laps times 7 minutes per lap. Since he runs at least 12 laps, the number of laps is \( \frac{t}{7} \) (because \( t = 7 \times \text{number of laps} \), so number of laps \( = \frac{t}{7} \)). "At least" means greater than or equal to, so \( \frac{t}{7} \geq 12 \).

Step2: Solve for \( t \)

Multiply both sides of the inequality \( \frac{t}{7} \geq 12 \) by 7 to isolate \( t \). We get \( t \geq 7\times12 \). Calculating \( 7\times12 = 84 \), so \( t \geq 84 \).

Answer:

\( t \geq 84 \)