Question
A coordinate plane for distance versus time.
Riley is training to run a 5-mile race. The graph represents the distance (miles) she ran with respect to time (minutes) in her first training run. Over which time interval did she run the fastest, [0,8]
or [2,11]
? Justify your answer in 1–2 sentences.
(2 points)
Riley is training to run a 5-mile race. The graph represents the distance (miles) she ran with respect to time (minutes) in her first training run. Over which time interval did she run the fastest, [0,8]
or [2,11]
? Justify your answer in 1–2 sentences.
(2 points)
Answers
GPT-4o mini
To determine the fastest interval, we need to compare the slopes of the distance versus time graph for the two given time intervals. The interval [0,8] can be analyzed by looking at the distance covered from the start to 8 minutes, while the interval [2,11] covers the distance from 2 minutes to 11 minutes.
Calculating the average speed (slope) for each interval, if the distance in [0,8] is, for example, 3 miles, the speed would be 3 miles / 8 minutes = 0.375 miles/minute. In the interval [2,11], if the distance covered is 4 miles, the speed would be 4 miles / 9 minutes = 0.444 miles/minute.
Thus, if the calculated speed for [2,11] is higher, Riley ran the fastest during that interval. Justify your conclusion with accurate data points from the graph, if applicable.
Calculating the average speed (slope) for each interval, if the distance in [0,8] is, for example, 3 miles, the speed would be 3 miles / 8 minutes = 0.375 miles/minute. In the interval [2,11], if the distance covered is 4 miles, the speed would be 4 miles / 9 minutes = 0.444 miles/minute.
Thus, if the calculated speed for [2,11] is higher, Riley ran the fastest during that interval. Justify your conclusion with accurate data points from the graph, if applicable.