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 22.5≤s≤25 22.5 less-than-or-equal-to s less-than-or-equal-to 25 5≤s

Question

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 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

GPT-4o mini · Answer

To determine when Kaitlyn reaches 1.25 miles during her workout, we can break down her activity step-by-step.

Slow Jog (5 minutes): Let’s denote her slow jog speed as \( v_1 \). We don't know \( v_1 \) yet, but we know she jogs for 5 minutes. In decimal hours, this is \( \frac{5}{60} = \frac{1}{12} \) hours.
Faster Pace (7 minutes): Let's denote her faster speed as \( v_2 \). She runs at this speed for 7 minutes, which is \( \frac{7}{60} \) hours.
Break (3 minutes): There is a break during which no distance is covered.
Final Run (7.5 minutes): Finally, she runs for 7.5 minutes at constant speed (let’s say \( v_3 \)), which is \( \frac{7.5}{60} = \frac{1.25}{10} = \frac{1}{8} \) hours.

The total distance covered by her can be described by the lengths of time she jogged at each rate of speed.

The distances covered can be calculated as follows:

Distance during slow jog: \[ d_1 = v_1 \times \frac{1}{12} \]
Distance during faster pace: \[ d_2 = v_2 \times \frac{7}{60} \]
Distance during final run: \[ d_3 = v_3 \times \frac{1}{8} \]

The total distance for the workout must equal 2 miles: \[ d_1 + d_2 + d_3 = 2 \]

When we want to find the point in time when Kaitlyn reaches 1.25 miles, we can also focus on the time taken for each segment of her workout. After each segment, we can add the distances until we reach 1.25 miles.

Let's assume \( v_1 \) (slow jog speed) is a placeholder as we don’t know its exact value. If she jogs at say, 6 mph during her slow jog,

\( d_1 = 6 \cdot \frac{1}{12} = 0.5 \) miles.

Then, if her faster pace (let's say 8 mph),

\( d_2 = 8 \cdot \frac{7}{60} = \frac{56}{60} = 0.9333 \) miles.

In total:

After slow jog: 0.5 miles
After faster pace: 0.5 + 0.9333 = 1.4333 miles

To reach 1.25 miles, she would reach this distance during her faster pace. Thus, following that, we can conclude that during strides:

From time \( 5 \) min (0.5 miles) to \( 12 \) min (1.4333 miles) is when she reaches 1.25 miles.

Thus, Kaitlyn reaches 1.25 miles within the time interval between 5 and 12 minutes into her workout:

The corresponding interval is 5 \leq s < 12.

Therefore, the correct response is: 5 ≤ s < 12.