Final answer:
To find out how many minutes it would take the athlete to run 18 km, the athlete's speed is first calculated in km/minute from the given mile time, and then the distance is divided by this speed, resulting in approximately 45.11 minutes.
Step-by-step explanation:
The question at hand is a problem involving rates and unit conversion. Given that an athlete runs a mile in 242.1 seconds, we can calculate the speed in a commonly used unit before finding out how long it would take them to run 18 km at the same speed.
First, we need to convert miles to kilometers. We know that 1 mile = 1.61 km. The athlete's speed in km/second is therefore 1.61 km / 242.1 seconds. Then, to convert the speed to km/minutes, we multiply by 60 seconds/minute, getting (1.61 km / 242.1 seconds) * (60 seconds / 1 minute).
Next, to determine the time in minutes it would take to run 18 km at this speed, we divide 18 km by the athlete's speed in km/minute.
The speed in km/minute: (1.61/242.1) * 60 = (1.61*60)/242.1 = 0.399 km/minute.
Time to run 18 km: 18 km / 0.399 km/minute = 45.11 minutes.
Therefore, it would take approximately 45.11 minutes for the athlete to run 18 kilometers at the same pace.