Final answer:
At least 1,250 rides are needed for 15,000 people to enjoy the thrill ride at an amusement park, considering the ride's capacity of 12 people per ride. It is unlikely that 15,000 people could ride in one day, given the short amount of time that would be available per ride.
Step-by-step explanation:
To answer part (a) of the question, let's let n represent the number of rides needed for 15,000 people to ride the thrill ride. Since the ride holds a maximum of 12 people, the inequality would be 12n ≥ 15,000. To solve for n, we divide both sides by 12, giving us n ≥ 15,000 / 12 which simplifies to n ≥ 1250. Therefore, at least 1,250 rides are necessary for 15,000 people to ride.
For part (b), to determine if it's possible for 15,000 people to ride in one day, we need to consider the ride's duration and operating hours. If the amusement park is open for 12 hours (720 minutes), each ride would need to last no more than 720 minutes / 1250 rides ≈ 0.576 minutes or approximately 34.56 seconds per ride when considering loading and unloading times. This seems very unlikely, as ride times are usually longer and we must account for the time taken to load and unload passengers. Thus, it is probably not possible for 15,000 people to ride the thrill ride in a single day.