Question
Polly is on a backpacking trip with her friends. They need to make it to the campground before sunset so that they have time to cook dinner and set up camp. There is a linear relationship between the time they spend hiking, in hours, and the distance from the campground, in miles. 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 x y Time (hours) Distance to campground (miles) Describe the rate of change for this relationship. The distance to the campground increases decreases by 1 2 of a mile 1mile 2miles 7miles 9miles 18miles per hour of hiking.
Answers
GPT-4o mini
To analyze the linear relationship between time spent hiking (in hours) and the distance to the campground (in miles), we’ll interpret the given data points. Since the values you've provided for time (x) and distance (y) appear to be in a simple linear progression, we can identify the rate of change by observing how the distance changes with respect to time.
Given the structure you described:
- Each time the x (time in hours) increases by 1, let's see how much the y (distance to the campground in miles) changes.
We can observe that as time progresses, for each additional hour spent hiking, the distance to the campground decreases, indicating they are getting closer to their destination.
From the options provided:
- The options you listed (1 mile, 2 miles, 7 miles, 9 miles, and 18 miles) indicate different potential rates of change.
1. If they were decreasing their distance by **1 mile per hour**, this means for every hour of hiking, they cover 1 mile.
2. If they were decreasing it by **2 miles per hour**, in the same time, they'd be getting twice as close.
3. And similarly for the other values.
To summarize the proper rate of change based on typical hiking patterns (considering reasonable paces under normal conditions):
The rate of change is likely to be **1 mile per hour** since this is a common hiking pace, which allows you to travel a sustainable distance while ensuring you have enough time to reach your destination (campground) before dusk.
Thus, the most reasonable rate of change would be **1 mile per hour** based on average hiking speeds and the context provided.
Given the structure you described:
- Each time the x (time in hours) increases by 1, let's see how much the y (distance to the campground in miles) changes.
We can observe that as time progresses, for each additional hour spent hiking, the distance to the campground decreases, indicating they are getting closer to their destination.
From the options provided:
- The options you listed (1 mile, 2 miles, 7 miles, 9 miles, and 18 miles) indicate different potential rates of change.
1. If they were decreasing their distance by **1 mile per hour**, this means for every hour of hiking, they cover 1 mile.
2. If they were decreasing it by **2 miles per hour**, in the same time, they'd be getting twice as close.
3. And similarly for the other values.
To summarize the proper rate of change based on typical hiking patterns (considering reasonable paces under normal conditions):
The rate of change is likely to be **1 mile per hour** since this is a common hiking pace, which allows you to travel a sustainable distance while ensuring you have enough time to reach your destination (campground) before dusk.
Thus, the most reasonable rate of change would be **1 mile per hour** based on average hiking speeds and the context provided.