To determine during which domain interval Kaitlyn reaches 1.25 miles during her run, we can analyze the sequence of her workout:
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Jogging at a constant rate for 5 minutes:
Let's say Kaitlyn jogs at a speed of \( V_1 \). For 5 minutes, she would cover a distance \( D_1 = V_1 \times 5 \). -
Increased speed for 7 minutes:
Now she runs faster at a speed of \( V_2 \) for 7 minutes, covering a distance \( D_2 = V_2 \times 7 \). -
Taking a 3-minute break:
No distance covered during this period. -
Running for another 7.5 minutes:
And then she runs at a speed \( V_3 \) for another 7.5 minutes, covering \( D_3 = V_3 \times 7.5 \). -
Resting for the remainder of the time.
Assuming Kaitlyn's total distance for her run is 2 miles, we can derive the equations for each section and check when she reaches 1.25 miles:
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In the jogging phase (first 5 minutes): If she jogs slowly, let’s assume for the sake of this problem that during this phase she may reach around \( 0.25 \) miles.
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In the increased speed phase (next 7 minutes): At a faster pace, she could cover an additional \( 0.5 \) miles. Cumulatively she would have covered \( 0.75 \) miles at the end of 12 minutes (5 minutes jogging + 7 minutes faster pace).
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After the 3-minute break: No extra distance is added.
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In the final running phase (7.5 minutes): If she covers \( 0.5 \) miles in this duration, by the end of this period, she might reach approximately \( 1.75 \) miles or more depending on her speed.
To find when she reaches exactly \( 1.25 \) miles, we can calculate it logically:
- By 12 minutes, she reaches \( 0.75 \) miles.
- Once she begins to run again for 7.5 minutes, she will definitely achieve 1.25 miles in this interval.
The interval during which she reaches 1.25 miles is most likely between 12 to 15 minutes.
Thus, the correct answer is: 12 ≤ s ≤ 15
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