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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 be at 1.25 miles?

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

(1 point)
Responses

22.5≤s≤25
22.5≤s≤25

5≤s<12
5≤s<12

12≤s≤15
12≤s≤15

15≤s≤22.5

1 answer

To determine during which time interval Kaitlyn was at 1.25 miles, we can break down her workout into parts and analyze her speed during those parts.

  1. First 5 minutes: She jogs at a slow constant rate. Let's assume her pace is moderate, completing some distance during these 5 minutes.

  2. Next 7 minutes: She speeds up and maintains a faster constant pace.

  3. 3-minute break: No distance covered.

  4. Last 7.5 minutes: She runs at her constant pace again to finish her run.

We need to determine her position at 1.25 miles during these time intervals.

  • In the first segment (5 minutes), if we assume she runs about 0.25 miles, then at 5 minutes she's approx 0.25 miles.
  • During the next segment (7 minutes), she may cover more distance, so by 12 minutes (5 min + 7 min), she might cover 0.75 miles in total or more depending on her speed.

Assuming she maintains a faster pace in the second part such that she hits 1.25 miles during the faster 7 minutes would make sense.

  • The total time includes the 3-minute break after the first 12 minutes. Therefore, she resumes running at the 15-minute mark for another 7.5 minutes, potentially surpassing the needed 1.25 miles before the end.

To find the exact interval, we can ascertain:

  • If she covers the first 0.5-1 miles in the first 12 minutes, the time interval when she reaches 1.25 miles is likely within the time just before the break or during the fast run. Since she is running for 7.5 minutes after her break, she would surpass 1.25 miles potentially during the first part of this final stretch.

Thus, based on the provided intervals:

  • Given the context, she would have hit 1.25 miles after the 12-minute mark but before she completes her second segment around 15 to potentially slightly over 22.5 depending on total pace.

Therefore, the appropriate answer would be:

15 ≤ s ≤ 22.5 (this interval encompasses her hitting 1.25 miles and beyond).