Riley is training to run a 5-mile race. The graph represents the distance (miles), or y, she ran with respect to time (minutes), or x, in her first training run. Over which time interval did she run the fastest, [0, 8] or [2, 11]? Justify your answer in 2 sentences.

Question

Points on graph: (0,0), (2,0.4), (8,1), (11,1.5).

Answer 1

To determine which time interval has the fastest running speed, we need to calculate the average speed for each interval.

For the interval [0, 8], Riley ran from 0 miles to 1 mile in 8 minutes, giving an average speed of 0.125 miles per minute. For the interval [2, 11], she ran from 0.4 miles to 1.5 miles in 9 minutes, which is 1.1 miles in 9 minutes, resulting in an average speed of approximately 0.122 miles per minute.

Thus, Riley ran faster during the interval [0, 8] since her average speed of 0.125 miles per minute is greater than her average speed of 0.122 miles per minute in the interval [2, 11].