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?
A.
only Otto's data
B.
both Jacob's data and Otto's data
C.
only Jacob's data
D.
neither Jacob's data nor Otto's data
To determine if the data shows a proportional relationship between the number of miles jogged and the time spent jogging, we can calculate the rates of Jacob and Otto's data.
For Jacob's data:
Rate on Wednesday = 3 miles / 30 minutes = 0.1 miles/minute
Rate on Thursday = 5 miles / 50 minutes = 0.1 miles/minute
For Otto's data:
Rate on Wednesday = 4 miles / 32 minutes = 0.125 miles/minute
Rate on Thursday = 6 miles / 50 minutes = 0.12 miles/minute
From the rates calculated, we can see that both Jacob's and Otto's rates are constant, or proportional. Therefore, the answer is B. both Jacob's data and Otto's data show a proportional relationship between the number of miles jogged and the time spent jogging.