On Friday, Kaitlyn went to the park to work out. She started with a slow job at a constant rate for five minutes. She then increased her speed to a fast, constant pace for seven minutes. She took a three-minute break, then ran for another 7.5 minutes at a constant pace to finish her two-mile run. She rested for the remainder of the time. During what domain interval will she reach 1.25 miles?
A. 12 _< s_< 15
B. 5 _< s < 12
C. 15 _< s_< 22.5
D. 22.5 _< s_< 25
First, we need to determine how far Kaitlyn runs during each part of her workout.
During the slow jog, Kaitlyn runs at a constant rate for 5 minutes. Since she runs at a constant rate, we can assume her speed is constant throughout the 5 minutes. Let's call her speed during this time period s1. The distance Kaitlyn runs during the slow jog is then 5s1.
During the fast pace, Kaitlyn runs at a constant rate for 7 minutes. Again, let's call her speed during this time period s2. The distance Kaitlyn runs during the fast pace is then 7s2.
After a 3-minute break, Kaitlyn runs for another 7.5 minutes at a constant pace. Let's call her speed during this time period s3. The distance Kaitlyn runs during this time period is then 7.5s3.
Adding up all these distances, we get the total distance Kaitlyn runs during her workout:
Distance = 5s1 + 7s2 + 7.5s3
Since Kaitlyn is running a total of 2 miles, we can set up the equation:
2 = 5s1 + 7s2 + 7.5s3
Now we need to determine the domain interval during which Kaitlyn reaches 1.25 miles. To do this, we can set up another equation:
1.25 = 5s1 + 7s2
Solving for s2, we get:
s2 = (1.25 - 5s1) / 7
Now, let's analyze the answer choices:
A. 12 _< s_< 15: This answer choice represents the domain interval for s2. However, since we need to find the domain interval for s1, this answer choice is incorrect.
B. 5 _< s < 12: This answer choice represents the domain interval for s2. Similarly, this answer choice is incorrect.
C. 15 _< s_< 22.5: This answer choice represents the domain interval for s2, which is not what we need. Therefore, this answer choice is incorrect.
D. 22.5 _< s_< 25: This answer choice represents the domain interval for s2, which is still not what we need. Therefore, this answer choice is also incorrect.
Based on the given answer choices, none of them represent the domain interval for s1. Therefore, the correct answer is none of the above.