Final answer:
After checking the ratios of distance to time for the given data, it is found that the ratios are not constant. Therefore, the relationship between time and distance in this case is not proportional.
Step-by-step explanation:
To determine whether the relationship between the time (in hours) and distance (in miles) presented is proportional, we need to check if the ratio of distance to time is constant for all given pairs of data. A proportional relationship means that for each increase in one variable, there is a consistent increase in the other variable which is described by the same ratio or fraction, essentially the 'rate of change' or 'slope' in the context of a graph. In this case, each change in time should correspond to the same change in distance at a constant rate. Let's calculate the ratios:
- For time 0.5 hours, distance = 20 miles, ratio = 20/0.5 = 40
- For time 1 hour, distance = 40 miles, ratio = 40/1 = 40
- For time 2 hours, distance = 60 miles, ratio = 60/2 = 30 (This ratio is different from the first two)
- For time 5 hours, distance = 80 miles, ratio = 80/5 = 16 (This ratio is different again)
Since the ratios are not consistent (they are not all the same), we can conclude that the relationship is not proportional.