After their noon rendezvous: One lady traveled some distance in 9 hours, and the other lady traveled some other distance in 4 hours. Before their noon rendezvous: you switch both the distances and the ladies. If x is the number of hours before noon that they traveled, you thus get that the ratio of 9 to x (what the first lady covered in 9 hours, the second covered in x) is that of x to 4 (what the first lady covered in x hours, the second covered in 4). Thus x is the geometric mean of 9 and 4, or in other words, x=6 and sunrise was 6 hours before noon at 6am.