Question

What is represented by the domain (0,12) in the context of the train's journey from Station 1 to its final destination 240 miles away from Station 2, given that the train travels at a constant rate of 15 miles per hour and there are no passengers waiting at Station 2?

Answer 1

The domain (0,12) in the context of the train's journey represents the time interval during which the train travels from Station 1 to the 240-mile distant final destination. It signifies the first 12 hours of the journey.

Step-by-step explanation:

Given that the train travels at a constant rate of 15 miles per hour, we can calculate the distance covered during the time interval (0,12). Using the formula d = rt, where d is the distance, r is the rate, and t is the time, we find that the train covers 15 x 12 = 180 miles during the first 12 hours. This corresponds to the distance covered in the given time interval (0,12).

Understanding the journey context, the train's final destination is 240 miles away from Station 2. As the train covers 180 miles in the first 12 hours, the remaining distance to the final destination is 240 - 180 = 60 miles. Therefore, the domain (0,12) represents the initial phase of the journey, during which the train covers 180 miles of the total 240-mile distance.

In conclusion, the domain (0,12) captures the time period when the train embarks on its journey, covering 180 miles within the first 12 hours. It offers a temporal perspective on the train's progress toward its final destination, providing insights into its initial phase of travel.

Answer 2

The domain (0,12) represents the time in hours from the start of the train's journey until it reaches the 12th hour, encompassing the initial phase of its travel.

Step-by-step explanation:

The given domain (0,12) signifies the time period in hours during which the train is in motion from Station 1 towards its final destination, which is 240 miles away from Station 2. The two values in the domain, 0 and 12, represent the starting and ending points of this specific segment of the journey. The constant rate of 15 miles per hour allows us to calculate the distance covered by the train during this interval. The distance covered can be determined by multiplying the rate (15 miles per hour) by the time (12 hours). In this case, 15 miles/hour * 12 hours = 180 miles.

Therefore, the train covers 180 miles during the time represented by the domain (0,12). This distance traveled reflects the initial part of the journey as the train moves steadily towards its final destination. The absence of passengers waiting at Station 2 indicates that the train does not make any stops during this time interval. Thus, the domain (0,12) encapsulates the early phase of the train's journey, providing a specific time frame for analysis within the overall context of the trip.