Christian went on a run. He jogged for five minutes, then increased his rate to a faster constant pace for seven minutes. He then took a rest for four minutes. During what time interval has Christian traveled 1.5 miles? (1 point) Christian traveled 1.5 miles from ()≤t≤() .

Answer 1

To determine the time interval during which Christian traveled 1.5 miles, we need to analyze the segments of his run.

1. Jogging Phase:

   • Christian jogged for 5 minutes.
   • Assume his jog pace is \( r_1 \) miles per minute.
   • The distance traveled during this phase is \( d_1 = r_1 \times 5 \).

2. Faster Pace:

   • After jogging, he ran faster for 7 minutes.
   • Let's assume his faster pace is \( r_2 \) miles per minute.
   • The distance traveled during this stage is \( d_2 = r_2 \times 7 \).

3. Rest Phase:

   • He took a rest for 4 minutes and did not travel any distance during this time.

Next, we need to calculate the total distance after the first two phases combined to determine at which point he reaches 1.5 miles.

To find the time intervals:

• If Christian jogs at a pace where the total distance (jogging + fast run) equals 1.5 miles, we can explore combinations. For instance:

  Let's say he jogs slower, at a pace of 0.1 miles per minute (this is just an example pace for calculation):

  • In 5 minutes, he would cover \( 0.1 \times 5 = 0.5 \) miles.

  If he runs faster at 0.25 miles per minute:

  • In 7 minutes, he would cover \( 0.25 \times 7 = 1.75 \) miles.

In this hypothetical example, after the jogging phase, he would have traveled 0.5 miles, and after the fast phase, he would have traveled 0.5 + 1.75 = 2.25 miles, which exceeds 1.5 miles.

Now we'll denote time intervals based on calculated distances. If he travels a total of 1.5 miles during these running phases:

Let’s adjust the example to meet the requirement of exactly 1.5 miles. If he perfectly needs to reach 1.5 miles in these intervals: Most likely, the balance of speeds and time intervals will demonstrate he may reach 1.5 miles during the faster running phase.

If he reaches precisely at the end of his jog and fasted run:

To summarize: Assuming realistic speeds where he closely meets 1.5 miles, we measure: 1.5 miles would be reached during jogging and potentially overlap as he runs, meaning we need to give appropriate speed assumptions.

Final answer: Christian traveled 1.5 miles from \( t = 0 \) to a certain point calculated based on his speed (likely around 10-12 minutes).

Thus it reads: Christian traveled 1.5 miles from \( (0 \leq t \leq x) \).