Question

1. Anneliese drove 23 miles in 28 minutes. Aaron drove 7 miles in 14 minutes.

2. Anneliese drove 18 miles in 27 minutes. Aaron drove 24 miles in 36 minutes.
3. Anneliese drove 9 miles in 21 minutes. Aaron drove 12 miles in 28 minutes.

Please indicate whether each ratio is proportional or not proportional.

Answer 1

After calculating rates for Anneliese and Aaron in each scenario, the first set of ratios is not proportional, while the second and third sets of ratios are proportional as they simplify to the same value.

Step-by-step explanation:

To determine if the ratios of distances driven to time taken are proportional between Anneliese and Aaron, we can compare their rates of driving for each scenario. Proportional ratios will have the same value when simplified.

Scenario Analysis

1. Anneliese's rate: 23 miles / 28 minutes = 0.8214 miles per minute. Aaron's rate: 7 miles / 14 minutes = 0.5 miles per minute. These ratios are not proportional.
2. Anneliese's rate: 18 miles / 27 minutes = 0.6667 miles per minute. Aaron's rate: 24 miles / 36 minutes = 0.6667 miles per minute. These ratios are proportional.
3. Anneliese's rate: 9 miles / 21 minutes = 0.4286 miles per minute. Aaron's rate: 12 miles / 28 minutes = 0.4286 miles per minute. These ratios are proportional.

When rates are the same or equivalent after simplification, the ratios are proportional. Otherwise, they are not proportional.