To analyze Blanca's performance, we want to find the average lap time for each day and the overall average lap time across all three days of practice.
### Day 1:
The lap times for Day 1 are: 83, 92, 91, 89, 94, 93, 88, 84
To find the average lap time for Day 1, we add up all the lap times and divide by the number of laps:
[tex]\[
\text{Average Day 1} = \frac{83 + 92 + 91 + 89 + 94 + 93 + 88 + 84}{8}
\][/tex]
We have already determined the sum:
[tex]\[
\text{Sum of Day 1 lap times} = 714
\][/tex]
So, the average for Day 1 is:
[tex]\[
\text{Average Day 1} = \frac{714}{8} = 89.25 \text{ seconds}
\][/tex]
### Day 2:
The lap times for Day 2 are: 87, 90, 92, 91, 92, 95, 90, 85
To find the average lap time for Day 2, we again add up all the lap times and divide by the number of laps:
[tex]\[
\text{Average Day 2} = \frac{87 + 90 + 92 + 91 + 92 + 95 + 90 + 85}{8}
\][/tex]
The sum of these lap times is:
[tex]\[
\text{Sum of Day 2 lap times} = 722
\][/tex]
So, the average for Day 2 is:
[tex]\[
\text{Average Day 2} = \frac{722}{8} = 90.25 \text{ seconds}
\][/tex]
### Day 3:
The lap times for Day 3 are: 85, 86, 91, 93, 91, 89, 88, 84
To find the average lap time for Day 3, we add up all the lap times and again divide by the number of laps:
[tex]\[
\text{Average Day 3} = \frac{85 + 86 + 91 + 93 + 91 + 89 + 88 + 84}{8}
\][/tex]
The sum of these lap times is:
[tex]\[
\text{Sum of Day 3 lap times} = 707
\][/tex]
So, the average for Day 3 is:
[tex]\[
\text{Average Day 3} = \frac{707}{8} = 88.375 \text{ seconds}
\][/tex]
### Overall Average:
To find the overall average lap time across all three days, we need to combine all the lap times and calculate the average:
The total sum of all lap times over the three days is:
[tex]\[
714 (\text{Day 1}) + 722 (\text{Day 2}) + 707 (\text{Day 3}) = 2143
\][/tex]
The total number of laps over the three days is:
[tex]\[
8 (\text{Day 1}) + 8 (\text{Day 2}) + 8 (\text{Day 3}) = 24
\][/tex]
So the overall average lap time is:
[tex]\[
\text{Overall Average} = \frac{2143}{24} \approx 89.2917 \text{ seconds}
\][/tex]
### Summary:
- Average Day 1 Lap Time: [tex]\( 89.25 \)[/tex] seconds
- Average Day 2 Lap Time: [tex]\( 90.25 \)[/tex] seconds
- Average Day 3 Lap Time: [tex]\( 88.375 \)[/tex] seconds
- Overall Average Lap Time: [tex]\( 89.2917 \)[/tex] seconds
These results give Blanca an idea of her pacing consistency and overall performance improvement over the three days of practice.
