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A piecewise linear function consisting of five parts is plotted in quadrant 1 of a coordinate plane.

On Friday, Kaitlyn went to the park to work out. She started with a slow jog at a constant rate for five minutes. She then increased her speed to a faster, 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?
(1 point)
Responses

5≤s<12

5 less-than-or-equal-to s less than 12
15≤s≤22.5
15 less-than-or-equal-to s less-than-or-equal-to 22.5
22.5≤s≤25
22.5 less-than-or-equal-to s less-than-or-equal-to 25
12≤s≤15

1 answer

To determine the domain interval during which Kaitlyn reaches 1.25 miles, we need to analyze her running and resting schedule.

  1. Initial Slow Jog (5 minutes): During this time, she runs at a slow constant rate. We need to find out how far she runs in this period.

  2. Increased Speed (7 minutes): She increases her speed for seven minutes. We'll calculate the distance covered in this interval as well.

  3. Break (3 minutes): She rests and does not cover any distance.

  4. Final Run (7.5 minutes): She runs the remaining distance to complete her two-mile run.

The total run time before she reaches 1.25 miles will involve combining these segments.

To find the exact domains:

  • For the first 5 minutes and the next 7 minutes, calculate the total distance covered until she reaches 1.25 miles.

Assuming constant speeds for each segment and a total time of 25 minutes for the entire workout, we can estimate that reaching 1.25 miles would most likely happen during the first two segments since that time span spans from 0 to 12 minutes.

We can provide a potential interval based on the information given: 12 ≤ s < 15 seems the most likely interval for her reaching 1.25 miles as she would have covered enough distance during her increased speed phase prior to her resting.

Thus, the correct interval is 12 ≤ s < 15.