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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
\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 :

GinnyAnswer
To find out which list correctly orders the runners from most improved to least improved, analyze the time differences compared to their personal best times. Improvement in time is measured as the difference from their personal best, where a more negative value means a better improvement (as they ran faster than their personal best).

We have the following time differences:
- Gregor: +5.6 (ran slower by 5.6 seconds compared to their personal best)
- Hiroki: -11.6 (ran faster by 11.6 seconds compared to their personal best)
- Isabelle: +3.2 (ran slower by 3.2 seconds compared to their personal best)
- Juan: 0 (ran exactly the same as their personal best)
- Karen: -5.2 (ran faster by 5.2 seconds compared to their personal best)

To order the runners from most improved to least improved, we need to start with the most negative values and move towards the most positive values:

1. Hiroki (-11.6): Most improved (fastest improvement).
2. Karen (-5.2): Second most improved.
3. Juan (0): No improvement or change.
4. Isabelle (+3.2): Slower by 3.2 seconds.
5. Gregor (+5.6): Least improved (slower by the most).

Therefore, the correct list from most improved to least improved is:

Hiroki, Karen, Juan, Isabelle, Gregor

So, the answer is:
Hiroki, Karen, Juan, Isabelle, Gregor

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