To determine if Jacob's and Otto's data show a proportional relationship between the number of miles jogged and the time spent jogging, we can calculate the rate (miles per minute) for both individuals on both days and see if they remain consistent.
Jacob's Data:
-
Wednesday: 3 miles in 30 minutes
- Rate = \( \frac{3 \text{ miles}}{30 \text{ minutes}} = 0.1 \text{ miles/minute} \)
-
Thursday: 5 miles in 50 minutes
- Rate = \( \frac{5 \text{ miles}}{50 \text{ minutes}} = 0.1 \text{ miles/minute} \)
Otto's Data:
-
Wednesday: 4 miles in 32 minutes
- Rate = \( \frac{4 \text{ miles}}{32 \text{ minutes}} = 0.125 \text{ miles/minute} \)
-
Thursday: 6 miles in 50 minutes
- Rate = \( \frac{6 \text{ miles}}{50 \text{ minutes}} = 0.12 \text{ miles/minute} \)
Now we can compare the rates:
- Jacob's rate is consistent at 0.1 miles/minute on both days.
- Otto's rates are different: 0.125 miles/minute on Wednesday and 0.12 miles/minute on Thursday.
Since Jacob has a constant rate and Otto does not, Jacob's data shows a proportional relationship between miles jogged and time spent jogging, while Otto's does not.
The answer is: D. only Jacob's data.
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