The given path can be illustrated in the following diagram:
She has only 30 miles worth of gas, if she comes back through the same path then the total distance is:

Therefore, she has not enough gas to go back using the same path.
Now, the total distance traveled in a straight path (SP) can be found using the Pythagorean theorem, we get:
![\begin{gathered} SP=\sqrt[]{13^2+24^2} \\ SP=\sqrt[]{745} \\ SP=27.3\text{ miles} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/htd068i9qu9fv0p3nsnzwkwfn9jfaqaeiw.png)
Therefore, she needs to take a straight path.