This is something that would fall into the category of an accident but whose fault would depend on a number of factors.  If the woman ran out of gas and she knew or had reason to know, then she would be at fault especially if you could not have seen her in time to stop.  If you could have stopped but didn't because you were speeding, then the costs may be split but understand this all depends on if your state follows contributory negligence or comparative negligence.  In essence, the difference could create liability in only one person or could create proportionate liability for both persons. Talk to a lawyer if you have not already done so and remember, there is always a statute of limitations issue to take into consideration if you plan on suing for damages to your vehicle or any medical damages you may have suffered.