Select the correct answer.

A team of swimmers is training for a swim meet. The table shows the number of laps each person has swum so far and how long the laps took.

\begin{tabular}{|l|r|r|}
\hline Name & Laps & Time (minutes) \\
\hline Jonathan & 2 & 4 \\
\hline Julian & 1 & 1 \\
\hline Seth & 3 & 6 \\
\hline Bennett & 7 & 21 \\
\hline Taylor & 4 & 7 \\
\hline
\end{tabular}

The relationship between time and the number of laps is not proportional across all swimmers. Which two swimmers swam at the same rate (had time and laps in the same proportion)?

A. Jonathan and Julian
B. Seth and Bennett
C. Julian and Taylor
D. Jonathan and Seth
E. Julian and Seth



Answer :

To determine which two swimmers swam at the same rate, we need to compute the rate of laps swum per minute for each swimmer. The rate can be calculated by dividing the number of laps by the time taken.

Let's calculate the rate for each swimmer:

1. Jonathan:
[tex]\[ \text{Rate} = \frac{\text{Laps}}{\text{Time}} = \frac{2}{4} = 0.5 \text{ laps per minute} \][/tex]

2. Julian:
[tex]\[ \text{Rate} = \frac{\text{Laps}}{\text{Time}} = \frac{1}{1} = 1 \text{ lap per minute} \][/tex]

3. Seth:
[tex]\[ \text{Rate} = \frac{\text{Laps}}{\text{Time}} = \frac{3}{6} = 0.5 \text{ laps per minute} \][/tex]

4. Bennett:
[tex]\[ \text{Rate} = \frac{\text{Laps}}{\text{Time}} = \frac{7}{21} = \frac{1}{3} \text{ laps per minute} \approx 0.333 \text{ laps per minute} \][/tex]

5. Taylor:
[tex]\[ \text{Rate} = \frac{\text{Laps}}{\text{Time}} = \frac{4}{7} \approx 0.571 \text{ laps per minute} \][/tex]

After calculating the rates, we compare them to find which two swimmers have the same rate:

- Jonathan: 0.5 laps per minute
- Julian: 1 lap per minute
- Seth: 0.5 laps per minute
- Bennett: ~0.333 laps per minute
- Taylor: ~0.571 laps per minute

We observe that Jonathan and Seth both have a rate of 0.5 laps per minute.

Therefore, the correct answer is:
D. Jonathan and Seth