Theo, Nancy, and Mary each drove seperately to meet at their grandmother's house for dinner. Theo drove 50 miles, Nancy drove \sqrt(2840) miles, and Mary's route is shown below.

To determine how far Mary drove and to compare the distances driven by Theo, Nancy, and Mary, we first need to calculate the distance Mary drove.

From the information given, we have:
- One part of Mary's route is \(13\) miles.
- The other part of Mary's route is \(48\) miles.

To find Mary's total distance, we add these two distances together:

\[
\text{Total distance Mary drove} = 13 \text{ miles} + 48 \text{ miles} = 61 \text{ miles}
\]

Next, let's calculate Nancy's driving distance, which is given as \(\sqrt{2840}\) miles:

1. Calculate \(\sqrt{2840}\):
- Breaking it down:
- \(2840 = 4 \times 710\)
- \(\sqrt{2840} = \sqrt{4 \times 710} = \sqrt{4} \times \sqrt{710} = 2\sqrt{710}\)

Now we can calculate an approximate value of \(\sqrt{710}\):
- Knowing that \(26^2 = 676\) and \(27^2 = 729\), we find that \(\sqrt{710}\) is between \(26\) and \(27\).
- Let's estimate it further:

Using a calculator, \(\sqrt{710} \approx 26.57\).
Thus,

\[
\sqrt{2840} \approx 2 \times 26.57 \approx 53.14 \text{ miles}
\]

Now we have the distances:
- Theo: \(50\) miles
- Nancy: \(\approx 53.14\) miles
- Mary: \(61\) miles

Now, we can order them from shortest to longest distance:
1. Theo: \(50\) miles
2. Nancy: \(\approx 53.14\) miles
3. Mary: \(61\) miles

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

**Theo, Nancy, Mary**.

To summarize:
- Mary drove approximately **61 miles**.
- The order of their drivers from shortest to longest is **Theo, Nancy, Mary**.