To calculate the average speed of the runner, we can use the formula for average speed:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
First, we need to find the total distance run over the three periods:
\[ \text{Total Distance} = 180 , \text{meters} + 188 , \text{meters} + 190 , \text{meters} = 558 , \text{meters} \]
Next, we calculate the total time. The runner recorded their distances over three separate time periods of 30 seconds, which means:
\[ \text{Total Time} = 30 , \text{seconds} + 30 , \text{seconds} + 30 , \text{seconds} = 90 , \text{seconds} \]
Now we can calculate the average speed:
\[ \text{Average Speed} = \frac{558 , \text{meters}}{90 , \text{seconds}} \approx 6.2 , \text{m/s} \]
Thus, the average speed of the runner is approximately 6.2 m/s.