The answer is black! when the third person is asked and said that she couldn't answer, she eliminates the posibility that the second and first one have two whites hats, in that case there's three posible scenarios:

• The second one has a white hat and the first one a black hat.
• The second one has a black hat and the first one a white hat.
• The second one has a black hat and the first one a black hat.

The only way the second one could've had the right answer is if she sees a white hat in the first lady, in that case she would've known for sure she had a black hat but since that didn't happen the first one concluded she was the one wearing the black hat!!!

It took me half hour and a piece of paper to solve it but it was fun! Cheers ;)