Final answer:
The college runner's average speed in kilometers per hour is 19.393 km/h when rounded to five significant figures and after converting the mile distance to kilometers and the time to hours.
Step-by-step explanation:
To calculate the average speed of the runner in kilometers per hour (km/h), we first convert the mile (which is equivalent to approximately 1.60934 kilometers) to kilometers and then divide this distance by the time taken to complete it. Since the time is given in minutes and seconds, we need to convert this to hours.
The runner's time is 3 minutes and 59.37 seconds. To convert this to hours, we use the conversion that 60 minutes equals 1 hour and 60 seconds equals 1 minute:
3 minutes is 3/60 hours.
59.37 seconds is 59.37/3600 hours.
Now add the converted minutes and seconds to get the total time in hours:
Time in hours = (3/60) + (59.37/3600) = 0.0665 + 0.01649 = 0.08299 hours (approximately).
The distance run is 1 mile, which is 1.60934 kilometers. Therefore:
Average speed = Distance / Time = 1.60934 km / 0.08299 h = 19.393 km/h (approximately).
Considering significant figures, since the time was measured to five significant figures, the speed should also be reflected with five significant figures. Thus, the runner's average speed is 19.393 km/h when rounded appropriately.
Lastly, let's check if the answer is reasonable by comparing it with known speeds. Since running a four-minute mile is a common benchmark for excellent runners, an average speed of around 20 km/h seems reasonable for a college athlete setting a school record.