Question

Theo, Nancy, and Mary each drove separately to meet at their grandmother's house for dinner. Theo drove 50 miles, Nancy drove 2840−−−−√
miles, and Mary's route is shown below.
side line is 48
bottom line is 13


Mary drove approximately
miles to her grandmother's house.

The order of their drives from shortest to longest is

Answer 1

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:
1. Mary: 49.73 miles (approximately)
2. Theo: 50 miles
3. Nancy: 53.33 miles (approximately)

Thus, the order of their drives from shortest to longest is:

**Mary, Theo, Nancy.**