Question

Tyler went to the park to work out. He started with a slow jog at a constant rate for five minutes. He then increased his speed to a faster, constant pace for seven minutes. He took a three-minute break, then ran for another 7.5 minutes at a constant pace to finish his two-mile run. He rested for the remainder of the time. During what domain interval is he at 0.75 miles? (1 point) Responses 15≤s≤22.5 15≤s≤22.5 12≤s≤15 12≤s≤15 5≤s<12 5≤s<12 22.5≤s≤25 22.5≤s≤25

Answer 1

To determine the time interval during which Tyler is at 0.75 miles during his run, we need to analyze his workout schedule step by step.

1. First 5 minutes: Tyler jogs at a slow pace. Let's assume his slow pace allows him to cover a distance of 0.4 miles in those 5 minutes. This establishes that in the first 5 minutes, he is between 0 and 0.4 miles.

2. Next 7 minutes: He increases his pace. To cover 0.6 miles, he would have to run at an appropriate faster pace. Let's say he runs the next segment to cover this distance. By the end of these 7 minutes (5 + 7 = 12 minutes total), he has covered a total of 0.4 + 0.6 = 1.0 mile.

3. 3-minute break: Tyler then takes a 3-minute break, meaning he is still at 1.0 mile during this time.

4. Final 7.5 minutes: After his break, he runs the remaining distance to complete 2 miles, which is 1 mile more. For simplicity, let's assume he runs this mile during the 7.5 minutes.

So far, after the first 12 minutes (including the break), he is at 1 mile. To reach 2 miles, he covers the last mile in 7.5 minutes, which occurs from 12 to 19.5 minutes after he started running.

Assuming Tyler's speeds allow him to reach 0.75 miles before he completes the 1.0 mile mark. Since he covers 0.4 miles in the first 5 minutes and has already reached 1.0 mile by 12 minutes, let's break down his speed between 5 minutes and 12 minutes.

To discover the specific timestamp for when he hits 0.75 miles:

• From 5 minutes to 12 minutes (0.4 miles to 1.0 mile): He covers 0.6 miles in 7 minutes, thus averaging \( \frac{0.6 \text{ miles}}{7 \text{ minutes}} = \approx 0.0857 \text{ miles per minute}\).

Now, let's find out when he reaches 0.75 miles.

• He starts at 0.4 miles at the 5-minute mark. To reach 0.75 miles:
  • Distance required = 0.75 - 0.4 = 0.35 miles.
  • Time taken to reach 0.75 miles at \( \approx 0.0857 \text{ miles per minute}\):
  • Time = \( \frac{0.35 \text{ miles}}{0.0857 \text{ miles per minute}} \approx 4.08\) minutes.

Therefore, from 5 minutes + 4.08 minutes = 9.08 minutes.

As such, Tyler is at 0.75 miles from approximately the 9 minute mark until he completes his jog at the 19.5 minutes.

Thus, you can assert that during the time interval when Tyler is at 0.75 miles is approximately between the 9-minute mark and time until he hits 1.0 mile at around 12 minutes, so the relevant interval is 5 ≤ s < 12.