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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

15 ≤ s ≤ 22.5
15 less-than-or-equal-to s less-than-or-equal-to 22.5

12 ≤ s ≤ 15
12 less-than-or-equal-to s less-than-or-equal-to 15

5 ≤ s < 12
5 less-than-or-equal-to s less than 12

22.5 ≤ s ≤ 25
22.5 less-than-or-equal-to s less-than-or-equal-to 25
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1 answer

To determine the domain interval during which Kaitlyn reaches 1.25 miles in her two-mile run, we need to analyze the provided information about her workout.

  1. Jogging: Kaitlyn jogged for 5 minutes at a constant speed.
  2. Faster Pace: She then increased her speed for 7 minutes.
  3. Break: She took a 3-minute break.
  4. Final Run: After the break, she ran for 7.5 minutes.

In total, this amounts to:

  • 5 minutes (slow jog)
  • 7 minutes (faster pace)
  • 3 minutes (break)
  • 7.5 minutes (final run)

This totals to 22.5 minutes of activity, with the 3-minute break included.

To find when she reaches 1.25 miles:

  • In the first segment (5 minutes of slow jogging), assume she covers some distance.
  • In the next segment (7 minutes), she likely covers a greater distance because of the faster pace.
  • After her short break and through 7.5 minutes of running, she would then cover additional distance.

Given the steady increase in speed after each segment, Kaitlyn will reach 1.25 miles after completing her first jogging segment and some additional time into her faster pace.

Therefore, if we consider the segments:

  • From the start to the end of the first jog (0 to 5 min), she will cover a certain distance.
  • In the next 7 minutes, if she maintains a faster pace, it will add to her distance cumulatively.

Without specific values for speed, the question implies finding a range after all these activities.

Since she jogs for the first 5 minutes, she would reach 1.25 miles sometime shortly after the initial jog and faster pace segments are completed but before she breaks and runs again.

From this analysis:

  1. She jogs (0 to 5 min), then goes to faster running (5 to 12 min), depending on her constant rates can be approximated to have hit 1 mile range very close beyond 15 min mark.
  2. Continuing to run, it'd be reasonable to assume she'd hit 1.25 miles before she reaches the 15-minute mark but definitely during her running segment.

Thus, looking at the options given and approximations of distances per minutes, the interval can be identified as:

15 ≤ s ≤ 22.5

So Kaitlyn would reach 1.25 miles between 15 and 22.5 minutes after she started her workout.