To determine which possible finishing time for Liz results in the median finishing time being 11 minutes 40 seconds, we need to follow these steps:
1. Convert the given finishing times into seconds for easier comparison:
- John: 12 minutes 20 seconds = [tex]\(12 \times 60 + 20 = 740\)[/tex] seconds
- Kiara: 11 minutes 40 seconds = [tex]\(11 \times 60 + 40 = 700\)[/tex] seconds
- Gina: 9 minutes 30 seconds = [tex]\(9 \times 60 + 30 = 570\)[/tex] seconds
- Hiro: 10 minutes 55 seconds = [tex]\(10 \times 60 + 55 = 655\)[/tex] seconds
2. Calculate the median time in seconds:
- Median time: 11 minutes 40 seconds = [tex]\(11 \times 60 + 40 = 700\)[/tex] seconds
3. Convert the possible times for Liz into seconds:
- 8 minutes 45 seconds = [tex]\(8 \times 60 + 45 = 525\)[/tex] seconds
- 10 minutes 20 seconds = [tex]\(10 \times 60 + 20 = 620\)[/tex] seconds
- 11 minutes 15 seconds = [tex]\(11 \times 60 + 15 = 675\)[/tex] seconds
- 14 minutes 10 seconds = [tex]\(14 \times 60 + 10 = 850\)[/tex] seconds
4. Determine which possible finishing time for Liz, when combined with the times of the other four students, results in a median time of 700 seconds.
- Trying 8 minutes 45 seconds (525 seconds):
- Sorted times: [525, 570, 655, 700, 740]
- Median: 655 (not 700)
- Trying 10 minutes 20 seconds (620 seconds):
- Sorted times: [570, 620, 655, 700, 740]
- Median: 655 (not 700)
- Trying 11 minutes 15 seconds (675 seconds):
- Sorted times: [570, 655, 675, 700, 740]
- Median: 675 (not 700)
- Trying 14 minutes 10 seconds (850 seconds):
- Sorted times: [570, 655, 700, 740, 850]
- Median: 700 (correct median)
Therefore, the possible finishing time for Liz that results in the median finishing time being 11 minutes 40 seconds is 14 minutes 10 seconds.
The best answer is:
14 minutes 10 seconds.
