To find the time interval in which Christian traveled 1.5 miles, we need to break down his run into segments and calculate how far he traveled in each segment.
-
First Segment (Jogging for 5 minutes): We don't have the jogging speed given, so let's denote it as \( r_1 \) miles per minute.
Distance traveled in the first segment: \[ \text{Distance}_1 = r_1 \times 5 , \text{minutes} = 5r_1 , \text{miles} \]
-
Second Segment (Faster pace for 7 minutes): Let's denote his faster pace as \( r_2 \) miles per minute.
Distance traveled in the second segment: \[ \text{Distance}_2 = r_2 \times 7 , \text{minutes} = 7r_2 , \text{miles} \]
-
During rest (4 minutes): During the rest, Christian does not travel any distance.
To find when he has traveled a total of 1.5 miles, we need to combine these distances:
Case 1: If he traveled 1.5 miles during the first segment only
We set the distance of the first segment equal to 1.5 miles: \[ 5r_1 = 1.5 \Rightarrow r_1 = \frac{1.5}{5} = 0.3 , \text{miles per minute} \]
This scenario is possible only if he traveled 1.5 miles in the first 5 minutes.
Case 2: If he traveled a portion in the first segment and then completed 1.5 miles in the second segment
Now, we will assume he traveled \( D_1 = 5r_1 \) in the first segment and \( D_2 = 7r_2 \) in the second segment such that: \[ D_1 + D_2 = 1.5 \] We can solve for distances but without exact rates, we can't get specific numbers.
However, if \( t = 5 + 7 = 12 \) minutes gives him exactly 1.5 miles, then we can find for intervals.
Assuming he travels enough in the second segment to surpass 1.5 miles:
Since Christian jogged for 5 minutes and then went faster for 7 minutes:
Total time interval:
- From \( t = 0 \) to \( t = 12 \) minutes for both segments, if he covered the distance adequately.
Result:
Christian traveled 1.5 miles during the time interval: \[ 0 \leq t \leq 12 \]
Thus, Christian traveled 1.5 miles from 0 ≤ t ≤ 12 minutes.
1 answer