To determine which interval Riley ran the fastest, we need to find the slope of the line segments represented by the points on the graph. The slope indicates the rate of distance covered per unit of time, which is the speed.
- Points on the graph:
- (0, 0) → (2, 0.4)
- (2, 0.4) → (8, 1)
- (8, 1) → (11, 1.5)
Let's calculate the speed (slope) for each interval:
-
Interval (0, 2):
- Distance = \(0.4 - 0 = 0.4\) miles
- Time = \(2 - 0 = 2\) minutes
- Speed = \(\frac{0.4}{2} = 0.2\) miles/minute
-
Interval (2, 8):
- Distance = \(1 - 0.4 = 0.6\) miles
- Time = \(8 - 2 = 6\) minutes
- Speed = \(\frac{0.6}{6} = 0.1\) miles/minute
-
Interval (8, 11):
- Distance = \(1.5 - 1 = 0.5\) miles
- Time = \(11 - 8 = 3\) minutes
- Speed = \(\frac{0.5}{3} \approx 0.1667\) miles/minute
Based on these calculations, the speeds for each interval are:
- (0, 2): 0.2 miles/minute
- (2, 8): 0.1 miles/minute
- (8, 11): approximately 0.1667 miles/minute
The fastest interval is (0, 2), with a speed of 0.2 miles/minute.
Therefore, the answer is (0, 2).
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