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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

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

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

1 answer

To determine the domain interval during which Kaitlyn reaches 1.25 miles, we will analyze her workout:

  1. First 5 minutes: Slow jog at a constant rate.
  2. Next 7 minutes: Increased speed at a faster constant pace.
  3. 3-minute break: No distance covered.
  4. Next 7.5 minutes: Running at a constant pace to complete the two-mile run.
  5. Remaining time: Resting.

Now, we need to assess how far Kaitlyn covered during each segment:

  • In the first 5 minutes, she jogs at a certain rate. We don't know the exact speed, so we have to assume it's relatively slow, and we will estimate she covers some distance, say \(d_1\).

  • In the next 7 minutes, she is at a faster pace. So in this time, she covers a larger distance, say \(d_2\).

  • After a 3-minute break, she runs for 7.5 minutes. By the end of all this running, she completes 2 miles.

To find out when she reaches 1.25 miles, we will need to break it down into parts.

Given the workout information:

  • The two-mile run takes a total of 22.5 minutes (5 + 7 + 3 + 7.5 = 22.5 minutes).

Assuming her speeds in each segment, we need to analyze the intervals based on her pace calculations.

If we proceed through the segments:

  • After 5 minutes (first jogging segment), let's say she has covered approximately \(d_1\) miles.
  • After 12 minutes (5 + 7 minutes), she has a combined distance of \(d_1 + d_2\).
  • Following the break, she runs for 7.5 more minutes.

Assuming all rates were sufficient to ensure she completes the 2 miles by the end of 22.5 minutes and reaches 1.25 miles during her speed increases, the time for 1.25 miles is likely to occur between her faster running segments.

Thus, after reviewing the options provided, the correct interval during which she reaches 1.25 miles is:

12 ≤ s ≤ 15