To determine the time interval over which Riley ran the fastest, we need to find the slope of the line segments between the points on the graph, as the slope represents the speed (distance per unit time) during those intervals.
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From (0,0) to (2,0.4):
- Change in distance: 0.4 - 0 = 0.4 miles
- Change in time: 2 - 0 = 2 minutes
- Slope = 0.4 miles / 2 minutes = 0.2 miles/min.
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From (2,0.4) to (8,1):
- Change in distance: 1 - 0.4 = 0.6 miles
- Change in time: 8 - 2 = 6 minutes
- Slope = 0.6 miles / 6 minutes = 0.1 miles/min.
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From (8,1) to (11,1.5):
- Change in distance: 1.5 - 1 = 0.5 miles
- Change in time: 11 - 8 = 3 minutes
- Slope = 0.5 miles / 3 minutes = approximately 0.17 miles/min.
Now we can compare the slopes:
- The fastest speed is during the interval [0, 2].
Therefore, Riley ran the fastest during the time interval [0, 2].