To find how far Mary drove, we first need to determine the length of her route, which can be represented as a right triangle with one side being 48 miles and the other side being 13 miles. We can use the Pythagorean theorem to calculate the hypotenuse (the distance Mary drove):
\[ c = \sqrt{a^2 + b^2} \]
where \(c\) is the hypotenuse, \(a\) is one side (13 miles), and \(b\) is the other side (48 miles).
Calculating:
\[ c = \sqrt{(13)^2 + (48)^2} = \sqrt{169 + 2304} = \sqrt{2473} \]
Now, estimating \(\sqrt{2473}\):
- The square root of 2400 is approximately 49 (since \(49^2 = 2401\)).
- The square root of 2500 is 50 (since \(50^2 = 2500\)).
So, \(\sqrt{2473}\) is slightly less than 50. We can use a calculator for more precision:
\[ \sqrt{2473} \approx 49.73 \]
Now, let's summarize the distances traveled:
- Theo: 50 miles
- Nancy: \(\sqrt{2840}\)
Now calculating Nancy's distance:
\[ \sqrt{2840} \approx 53.33 \text{ (since \(53.33^2 \approx 2840\))} \]
With these distances:
- Mary: approximately 49.73 miles
- Theo: 50 miles
- Nancy: approximately 53.33 miles
Now we can order these distances from shortest to longest:
- Mary: 49.73 miles (approximately)
- Theo: 50 miles
- Nancy: 53.33 miles (approximately)
Thus, the order of their drives from shortest to longest is:
Mary, Theo, Nancy.
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