distance time

Question

2
1.8
1.6
1.4 (11,1.5)
1.2
1 (8,1)
0.8
0.6
0.4
0.2 (2,0.4)
0 (0,0)
0 2 4 6 8 10 12 14 16
time / minutes

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 interval did she run the fastest?

(1 point)
Responses

[0, 8]
[0, 8]

[2, 11]
[2, 11]

[0, 2]
[0, 2]

[2, 8]

Answer 1

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.

1. Interval [0, 2]:

   • Distance changes from 0 to 0.4 miles.
   • Speed = (0.4 - 0)/(2 - 0) = 0.2 miles/minute.

2. Interval [2, 8]:

   • Distance changes from 0.4 to 1 mile.
   • Speed = (1 - 0.4)/(8 - 2) = 0.6/6 = 0.1 miles/minute.

3. Interval [2, 11]:

   • Distance changes from 1 to 1.5 miles.
   • Speed = (1.5 - 1)/(11 - 2) = 0.5/9 ≈ 0.0556 miles/minute.

4. 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]