Question

Joseph, Colby, and Susie are training for a marathon. On Saturday, Joseph ran 125−−−√ miles, Colby ran 13 miles, and Susie ran the direct path from the library to her house. Which list shows the names in order from the person who ran the shortest distance to the person who ran the longest distance?(1 point)ResponsesColby, Joseph, SusieColby, Joseph, SusieSusie, Colby, JosephSusie, Colby, JosephSusie, Joseph, ColbySusie, Joseph, ColbyJoseph, Colby, Susie

Answer 1

First, let's calculate the distances run by Joseph:

Joseph ran \( \sqrt{125} \) miles. We can simplify this as follows:

\[
\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}
\]

To find a numerical value for \( 5\sqrt{5} \), we can estimate \( \sqrt{5} \):

\[
\sqrt{5} \approx 2.236
\]
Thus,
\[
5\sqrt{5} \approx 5 \times 2.236 \approx 11.18 \text{ miles}
\]

Now we can compare the distances:

- Joseph ran approximately \( 11.18 \) miles.
- Colby ran \( 13 \) miles.
- Susie's distance is unknown, as it wasn't given a numerical value, but it's implied that her distance is longer than both Joseph's and Colby's for the sake of this list (considering general marathon training practices).

Now to arrange them from shortest to longest distance:

1. Joseph: \( 11.18 \) miles
2. Colby: \( 13 \) miles
3. Susie: unknown but presumably longer than Colby

Thus, the order from the shortest distance to the longest distance is:

**Joseph, Colby, Susie**

The correct answer is:
**Joseph, Colby, Susie**.