Keep trying, if you don't have it yet. Will post answer on continuation page, below:
If they all saw at least one red hat, the only two possibilities could be RRR and RRW. That was the dilemma.
However, if any one of them saw a white hat, she would know immediately that she must have a red hat. That decision would take no time at all.
The quickest-thinking one realized, when no-one else answered promptly, that it must be RRR. Therefore, the time delay of these brainy gals indicates that they all must have had red hats.