To determine the distances driven by each person and to arrange them from shortest to longest, we need to calculate the approximate value of Nancy's distance and then analyze the information given about Mary's route.
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Theo's distance: 50 miles.
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Nancy's distance: We need to calculate \( \sqrt{2840} \). \[ \sqrt{2840} \approx 53.3 \text{ miles} \] (Since \( \sqrt{2800} \) is about \( 52.9 \), and \( \sqrt{2890} \) is about \( 53.8 \), the value of \( \sqrt{2840} \) is approximately \( 53.3 \).)
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Mary's distance: We don't have the specific distance provided in the question, but we will assume you have some data to calculate it. Let's denote Mary's distance as \( M \).
Next, we will order the distances:
- Theo: 50 miles
- Nancy: \( \sqrt{2840} \approx 53.3 \) miles
- Mary: \( M \) miles (unknown)
To order them from shortest to longest, we would need Mary's exact distance in miles. Without that, here’s a possible way to display:
If for example Mary drove
- less than 50 miles: Shortest to Longest: Mary < Theo < Nancy
- exactly 50 miles: Shortest to Longest: Theo = Mary < Nancy
- between 50 miles and approximately 53.3 miles: Shortest to Longest: Theo < Mary < Nancy
- greater than approximately 53.3 miles: Shortest to Longest: Theo < Nancy < Mary
Once you have Mary's distance, simply replace \( M \) with that value and follow the same logic to order the distances accurately.