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Sagot :
Let's determine the pace for each driver based on their mileage and time information. The pace can be calculated as the distance traveled (in miles) divided by the time taken (in seconds).
Given data:
- Adam: Mileage = [tex]\(68 \frac{5}{8}\)[/tex] miles, Time = 1 hour, 49 minutes, 48 seconds.
- Allen: Mileage = [tex]\(58 \frac{4}{5}\)[/tex] miles, Time = 1 hour, 36 minutes, 0 seconds.
- Nigel: Mileage = [tex]\(32 \frac{3}{10}\)[/tex] miles, Time = 0 hours, 51 minutes, 0 seconds.
- Owen: Mileage = [tex]\(44 \frac{1}{10}\)[/tex] miles, Time = 1 hour, 12 minutes, 0 seconds.
- William: Mileage = [tex]\(54 \frac{3}{8}\)[/tex] miles, Time = 1 hour, 27 minutes, 0 seconds.
First, convert the times into seconds:
1. Adam:
- Time: 1 hour 49 minutes 48 seconds = [tex]\(1 \times 3600 + 49 \times 60 + 48 = 6588\)[/tex] seconds.
- Mileage: [tex]\(68 \frac{5}{8} = 68.625\)[/tex] miles.
2. Allen:
- Time: 1 hour 36 minutes 0 seconds = [tex]\(1 \times 3600 + 36 \times 60 + 0 = 5760\)[/tex] seconds.
- Mileage: [tex]\(58 \frac{4}{5} = 58.8\)[/tex] miles.
3. Nigel:
- Time: 0 hours 51 minutes 0 seconds = [tex]\(0 \times 3600 + 51 \times 60 + 0 = 3060\)[/tex] seconds.
- Mileage: [tex]\(32 \frac{3}{10} = 32.3\)[/tex] miles.
4. Owen:
- Time: 1 hour 12 minutes 0 seconds = [tex]\(1 \times 3600 + 12 \times 60 + 0 = 4320\)[/tex] seconds.
- Mileage: [tex]\(44 \frac{1}{10} = 44.1\)[/tex] miles.
5. William:
- Time: 1 hour 27 minutes 0 seconds = [tex]\(1 \times 3600 + 27 \times 60 + 0 = 5220\)[/tex] seconds.
- Mileage: [tex]\(54 \frac{3}{8} = 54.375\)[/tex] miles.
Next, calculate the pace (miles per second) for each driver:
1. Adam:
- Pace = Mileage / Time = [tex]\(68.625 / 6588 \approx 0.01042\)[/tex].
2. Allen:
- Pace = Mileage / Time = [tex]\(58.8 / 5760 \approx 0.01021\)[/tex].
3. Nigel:
- Pace = Mileage / Time = [tex]\(32.3 / 3060 \approx 0.01056\)[/tex].
4. Owen:
- Pace = Mileage / Time = [tex]\(44.1 / 4320 \approx 0.01021\)[/tex].
5. William:
- Pace = Mileage / Time = [tex]\(54.375 / 5220 \approx 0.01042\)[/tex].
From the calculations, we find that:
- Adam and William have the same pace ([tex]\(\approx 0.01042\)[/tex] miles per second).
- Allen and Owen have the same pace ([tex]\(\approx 0.01021\)[/tex] miles per second).
Thus, the correct sets of drivers progressing at the same pace are:
- Adam and William
- Allen and Owen
Given data:
- Adam: Mileage = [tex]\(68 \frac{5}{8}\)[/tex] miles, Time = 1 hour, 49 minutes, 48 seconds.
- Allen: Mileage = [tex]\(58 \frac{4}{5}\)[/tex] miles, Time = 1 hour, 36 minutes, 0 seconds.
- Nigel: Mileage = [tex]\(32 \frac{3}{10}\)[/tex] miles, Time = 0 hours, 51 minutes, 0 seconds.
- Owen: Mileage = [tex]\(44 \frac{1}{10}\)[/tex] miles, Time = 1 hour, 12 minutes, 0 seconds.
- William: Mileage = [tex]\(54 \frac{3}{8}\)[/tex] miles, Time = 1 hour, 27 minutes, 0 seconds.
First, convert the times into seconds:
1. Adam:
- Time: 1 hour 49 minutes 48 seconds = [tex]\(1 \times 3600 + 49 \times 60 + 48 = 6588\)[/tex] seconds.
- Mileage: [tex]\(68 \frac{5}{8} = 68.625\)[/tex] miles.
2. Allen:
- Time: 1 hour 36 minutes 0 seconds = [tex]\(1 \times 3600 + 36 \times 60 + 0 = 5760\)[/tex] seconds.
- Mileage: [tex]\(58 \frac{4}{5} = 58.8\)[/tex] miles.
3. Nigel:
- Time: 0 hours 51 minutes 0 seconds = [tex]\(0 \times 3600 + 51 \times 60 + 0 = 3060\)[/tex] seconds.
- Mileage: [tex]\(32 \frac{3}{10} = 32.3\)[/tex] miles.
4. Owen:
- Time: 1 hour 12 minutes 0 seconds = [tex]\(1 \times 3600 + 12 \times 60 + 0 = 4320\)[/tex] seconds.
- Mileage: [tex]\(44 \frac{1}{10} = 44.1\)[/tex] miles.
5. William:
- Time: 1 hour 27 minutes 0 seconds = [tex]\(1 \times 3600 + 27 \times 60 + 0 = 5220\)[/tex] seconds.
- Mileage: [tex]\(54 \frac{3}{8} = 54.375\)[/tex] miles.
Next, calculate the pace (miles per second) for each driver:
1. Adam:
- Pace = Mileage / Time = [tex]\(68.625 / 6588 \approx 0.01042\)[/tex].
2. Allen:
- Pace = Mileage / Time = [tex]\(58.8 / 5760 \approx 0.01021\)[/tex].
3. Nigel:
- Pace = Mileage / Time = [tex]\(32.3 / 3060 \approx 0.01056\)[/tex].
4. Owen:
- Pace = Mileage / Time = [tex]\(44.1 / 4320 \approx 0.01021\)[/tex].
5. William:
- Pace = Mileage / Time = [tex]\(54.375 / 5220 \approx 0.01042\)[/tex].
From the calculations, we find that:
- Adam and William have the same pace ([tex]\(\approx 0.01042\)[/tex] miles per second).
- Allen and Owen have the same pace ([tex]\(\approx 0.01021\)[/tex] miles per second).
Thus, the correct sets of drivers progressing at the same pace are:
- Adam and William
- Allen and Owen
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