Coach DeCaro records the cross-country runners' times compared to their personal best times.

\begin{tabular}{|c|c|}
\hline \multicolumn{2}{|c|}{ 3K Times } \\
\hline Runner & \begin{tabular}{c}
Time compared to \\
personal best
\end{tabular} \\
\hline Gregor & +5.6 \\
\hline Hiroki & -11.6 \\
\hline Isabelle & +3.2 \\
\hline Juan & 0 \\
\hline Karen & -5.2 \\
\hline \hline
\end{tabular}

Which list correctly orders the runners from MOST improved to LEAST improved?

A. Hiroki, Karen, Juan, Isabelle, Gregor
B. Juan, Hiroki, Karen, Isabelle, Gregor
C. Juan, Isabelle, Karen, Gregor, Hiroki
D. Gregor, Isabelle, Juan, Karen, Hiroki



Answer :

To determine the order of the runners from most improved to least improved, we need to consider their times compared to their personal bests. A negative number indicates an improvement, and a positive number indicates a slower time compared to their personal best.

Here are the times:

- Gregor: +5.6 (5.6 seconds slower than his personal best)
- Hiroki: -11.6 (11.6 seconds faster than his personal best)
- Isabelle: +3.2 (3.2 seconds slower than her personal best)
- Juan: 0 (equal to his personal best)
- Karen: -5.2 (5.2 seconds faster than her personal best)

To rank them from most improved to least improved:

1. Hiroki: -11.6 (most improved, since his time is the fastest compared to his personal best)
2. Karen: -5.2 (second most improved, also faster but not as much as Hiroki)
3. Juan: 0 (no improvement, but no decline either)
4. Isabelle: +3.2 (slower than personal best, less decline than Gregor)
5. Gregor: +5.6 (least improved, slowest compared to his personal best)

Thus, the correct order from most improved to least improved is:

Hiroki, Karen, Juan, Isabelle, Gregor

Hence, the correct list is:
```
Hiroki, Karen, Juan, Isabelle, Gregor
```