A coach is comparing data about the number of miles Jacob and Otto jogged and the time they spent jogging on week days.
Jacob jogged 3 miles in 30 minutes on Wednesday and 5 miles in 50 minutes on Thursday. Otto jogged 4 miles in 32 minutes on Wednesday and 6 miles in 50 minutes on Thursday.
Whose data shows a proportional relationship between the number of miles jogged and the time spent jogging?
To determine whose data shows a proportional relationship between the number of miles jogged and the time spent jogging, we need to compare the ratios of miles jogged to time spent jogging for each person.
For Jacob:
- On Wednesday, he jogged 3 miles in 30 minutes, so the ratio is 3/30 = 1/10.
- On Thursday, he jogged 5 miles in 50 minutes, so the ratio is 5/50 = 1/10.
For Otto:
- On Wednesday, he jogged 4 miles in 32 minutes, so the ratio is 4/32 = 1/8.
- On Thursday, he jogged 6 miles in 50 minutes, so the ratio is 6/50 = 3/25.
As we can see, only Jacob's ratios are the same for both days. Therefore, Jacob's data shows a proportional relationship between the number of miles jogged and the time spent jogging.