If a was her acceleration during the first 3 sec, what was her speed and distance after those three seconds (in terms of a)? If her speed remained constant during the next 8.8 sec, what was her additional distance during those 8.8 sec(in terms of a)? In terms of a, what was her total distance?

Total distance is 100 m, she ran 100 m in 11.8 s, she had constant acceleration during the first 3 s after that(the remaining 8.8 s) she had constant v.

[itex]s = vt[/itex]
[itex]s = \frac{1}{2}at^2[/itex]
A combination of the two is what I suspect to be the correct formula

Good. Now all you need to do is substitute the relationship for v as a function of a and t_{1}. (v doesn't change after the initial 3 seconds). This will give you what you need to solve for a.