imc

In order to get the smallest palindrome greater than $15951$, we need to raise the middle digit. If we were to raise any of the digits after the middle, we would be forced to also raise a digit before the middle to keep it a palindrome, making it unnecessarily larger. So we raise $9$ to the next largest value, $10$, but obviously, that's not how place value works, so we're in the $16000$s now. To keep this a palindrome, our number is now $16061$. So Megan drove $16061-15951=110$ miles. Since this happened over $2$ hours, she drove at $\frac{110}{2}=\boxed{55}$ mph.