A coordinate plane for distance versus time.

Question

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)

Answer 1

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.