To determine the interval where Riley ran the fastest, we need to look at the slope of the graph during each interval. The slope represents her speed; a steeper slope indicates a faster pace.
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Interval [0, 2]:
- Distance changes from 0 to 0.4 miles.
- Speed = (0.4 - 0)/(2 - 0) = 0.2 miles/minute.
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Interval [2, 8]:
- Distance changes from 0.4 to 1 mile.
- Speed = (1 - 0.4)/(8 - 2) = 0.6/6 = 0.1 miles/minute.
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Interval [2, 11]:
- Distance changes from 1 to 1.5 miles.
- Speed = (1.5 - 1)/(11 - 2) = 0.5/9 ≈ 0.0556 miles/minute.
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Interval [0, 8]:
- Distance changes from 0 to 1 mile.
- Speed = (1 - 0)/(8 - 0) = 1/8 = 0.125 miles/minute.
From these calculations, we can compare the speeds:
- [0, 2]: 0.2 miles/minute
- [2, 8]: 0.1 miles/minute
- [2, 11]: 0.0556 miles/minute
- [0, 8]: 0.125 miles/minute
The fastest speed was during the interval [0, 2] where the speed was 0.2 miles/minute.
Therefore, the answer is:
[0, 2]