To determine whether the data shows a proportional relationship, we need to calculate the ratio of miles jogged to time spent for both Jacob and Otto on each day.
Jacob's data:
- Wednesday: 3 miles in 30 minutes \[ \text{Ratio} = \frac{3 \text{ miles}}{30 \text{ minutes}} = \frac{3}{30} = \frac{1}{10} \text{ miles per minute} \]
- Thursday: 5 miles in 50 minutes \[ \text{Ratio} = \frac{5 \text{ miles}}{50 \text{ minutes}} = \frac{5}{50} = \frac{1}{10} \text{ miles per minute} \]
Both days for Jacob give a consistent ratio of \( \frac{1}{10} \), indicating a proportional relationship.
Otto's data:
- Wednesday: 4 miles in 32 minutes \[ \text{Ratio} = \frac{4 \text{ miles}}{32 \text{ minutes}} = \frac{4}{32} = \frac{1}{8} \text{ miles per minute} \]
- Thursday: 6 miles in 50 minutes \[ \text{Ratio} = \frac{6 \text{ miles}}{50 \text{ minutes}} = \frac{6}{50} = \frac{3}{25} = 0.12 \text{ miles per minute} \]
These two ratios for Otto are \( \frac{1}{8} \) (0.125) and \( \frac{3}{25} \) (0.12), which are not equal, indicating that his data does not show a proportional relationship.
Since Jacob's data shows a consistent ratio while Otto's data does not, the answer is:
D. only Jacob's data
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