Say the middle point is M. We know that for each person the ratio of time to go between M->A should be the same as to go between M->B since the distance is fixed only the rates are different.
First lady got to B at 4 pm so her M->B is 4. Second lady got to A at 9 pm so her M->B is 9. Since they both left in the morning, if we call the first lady's M->A time to be x, we know that the second lady's M->B has to be x as well.
Using the fact that the ratio of M->A : M->B should be the same for both of them, we can set up the equation
4/x = x/9 ==> x^2 = 36 ==> x = 6
Since getting to M was at noon and 12-6=6, dawn was at 6 am.
(For what it's worth, I did trial and error too cause I was lazy and didn't feel like thinking... then noticed the nice pattern and back justified it. :P)
First lady got to B at 4 pm so her M->B is 4. Second lady got to A at 9 pm so her M->B is 9. Since they both left in the morning, if we call the first lady's M->A time to be x, we know that the second lady's M->B has to be x as well.
Using the fact that the ratio of M->A : M->B should be the same for both of them, we can set up the equation
4/x = x/9 ==> x^2 = 36 ==> x = 6
Since getting to M was at noon and 12-6=6, dawn was at 6 am.
(For what it's worth, I did trial and error too cause I was lazy and didn't feel like thinking... then noticed the nice pattern and back justified it. :P)