Question

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 time interval did she run the fastest. The points are as follows: (0, 0), (2, 0.4), (8, 1), (11, 1.5)

Answer 1

To determine the time interval during which Riley ran the fastest, we need to calculate the average speed (distance per time) over the intervals defined by the points given.

The points you provided are:
1. (0, 0) – At 0 minutes, she has run 0 miles.
2. (2, 0.4) – At 2 minutes, she has run 0.4 miles.
3. (8, 1) – At 8 minutes, she has run 1 mile.
4. (11, 1.5) – At 11 minutes, she has run 1.5 miles.

Now let's calculate the average speed over each time interval:

1. **Interval from (0, 0) to (2, 0.4)**:
- Distance: 0.4 miles - 0 miles = 0.4 miles
- Time: 2 minutes - 0 minutes = 2 minutes
- Average Speed = Distance / Time = 0.4 miles / 2 minutes = 0.2 miles/minute.

2. **Interval from (2, 0.4) to (8, 1)**:
- Distance: 1 mile - 0.4 miles = 0.6 miles
- Time: 8 minutes - 2 minutes = 6 minutes
- Average Speed = 0.6 miles / 6 minutes = 0.1 miles/minute.

3. **Interval from (8, 1) to (11, 1.5)**:
- Distance: 1.5 miles - 1 mile = 0.5 miles
- Time: 11 minutes - 8 minutes = 3 minutes
- Average Speed = 0.5 miles / 3 minutes ≈ 0.167 miles/minute.

Now, let's summarize the average speeds:
- From 0 to 2 minutes: 0.2 miles/minute
- From 2 to 8 minutes: 0.1 miles/minute
- From 8 to 11 minutes: ≈ 0.167 miles/minute

The fastest interval is from \(0\) to \(2\) minutes where she ran at an average speed of \(0.2\) miles/minute.

Therefore, **Riley ran the fastest in the time interval from 0 to 2 minutes**.