8.) You run 18 laps in 9 minutes. Your friend runs 34 laps in 17 minutes. Are the rates equivalent? (prove it)

To determine if the running rates of you and your friend are equivalent, we need to calculate the rate of laps per minute for both of you. ### Step 1: Calculate your rate You run 18 laps in 9 minutes. The rate \( R_1 \) can be calculated as follows: \[ R_1 = \frac{\text{laps}}{\text{time}} = \frac{18 \text{ laps}}{9 \text{ minutes}} = 2 \text{ laps per minute} \] ### Step 2: Calculate your friend's rate Your friend runs 34 laps in 17 minutes. The rate \( R_2 \) can be calculated as follows: \[ R_2 = \frac{\text{laps}}{\text{time}} = \frac{34 \text{ laps}}{17 \text{ minutes}} = 2 \text{ laps per minute} \] ### Step 3: Compare the rates Now we compare the two rates: - Your rate \( R_1 = 2 \text{ laps per minute} \) - Your friend's rate \( R_2 = 2 \text{ laps per minute} \) Since both rates are equal, we can conclude that the rates are equivalent. ### Conclusion Yes, the rates are equivalent, as both you and your friend run at a rate of 2 laps per minute.