Directions: Select all the correct answers.

In the Trans-Yukon Rally Race, each team's finish is determined by their individual time to complete the course. There are five teams sponsored by American motor companies. The drivers of the American teams, their current mileage into the race, and their official times at that point in the race are listed in the table below.

\begin{tabular}{|c|c|c|}
\hline Name & Mileage & \begin{tabular}{c}
Time \\
(hours:minutes:seconds)
\end{tabular} \\
\hline Adam & [tex]$68 \frac{5}{8}$[/tex] & [tex]$1:49:48$[/tex] \\
\hline Allen & [tex]$58 \frac{4}{5}$[/tex] & [tex]$1:36:00$[/tex] \\
\hline Nigel & [tex]$32 \frac{3}{10}$[/tex] & [tex]$0:51:00$[/tex] \\
\hline Owen & [tex]$44 \frac{1}{10}$[/tex] & [tex]$1:12:00$[/tex] \\
\hline William & [tex]$54 \frac{3}{8}$[/tex] & [tex]$1:27:00$[/tex] \\
\hline
\end{tabular}

Which sets of drivers are progressing at the same pace?

A. Allen and Owen

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