No, they are not equivalent.
In order to find the rates, take the number of laps, in this case, 18, and divide by the time, in this case, 9 minutes. 18/9=2. So, you run 2 laps every minute.
For the other rate, your friend's, do the same. Take 24 and divide by 6. 24/6=4. So, your friend runs 4 laps every minute.
Your friend is faster, and the rates are not equivalent.