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Question

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

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

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

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

Answer 1

To determine the time interval during which Kaitlyn reaches 1.25 miles, we can analyze her workout plan step-by-step:

1. Slow jog for 5 minutes:

   • Distance covered: Assuming a slow jog pace of around 4 mph, in 5 minutes (1/12 of an hour), she would cover approximately \( \frac{4 \text{ miles per hour} \times \frac{1}{12} \text{ hours}}{1} = \frac{1}{3} \) miles.

2. Increased speed for 7 minutes:

   • Let's assume she increases her speed to about 6 mph for this interval. In 7 minutes (7/60 hours), she would cover approximately \( \frac{6 \text{ miles per hour} \times \frac{7}{60} \text{ hours}}{1} = 0.7 \) miles. This brings her total distance to about \( \frac{1}{3} + 0.7 \approx 1.03 \) miles.

3. Break for 3 minutes:

   • No distance is covered during the break.

4. Running for 7.5 minutes:

   • She could increase her pace again to 8 mph. In 7.5 minutes (7.5/60 hours), she would run \( \frac{8 \text{ miles per hour} \times \frac{7.5}{60}}{1} = 1 \) miles. Adding this to her previous distance, she would then have approximately \( 1.03 + 1 = 2.03 \) miles, thus completing more than 2 miles.

Now we will analyze the timeline if she reaches 1.25 miles during her workout:

• At 5 minutes, she's covered approximately \( \frac{1}{3} \) miles.
• At 12 minutes (5 + 7), she reaches approximately \( 1.03 \) miles.
• In her next 7.5 minutes, she would gain another mile.

Given that the function must be in a piecewise linear format for the whole duration and that she transitions from 1.03 to more than 2 miles in the time she works out (from minute 12 to 19.5), she likely hits the 1.25-mile mark somewhere between 12 and 15 minutes.

Thus, the correct interval during which Kaitlyn reaches 1.25 miles is:

12 ≤ s ≤ 15