[artemisyna]

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)

[ghosty141]

The text is confusing to me.

>and each of them carried on walking with the same speed

I thought the "same speed" meant lady1's speed = lady2's which made no sense...

[misterprime]

That's exactly how I read it. It was the first obstacle to overcome. "OK, they're walking different speeds, and the statement means that neither of them changed their own unique speed over the course of their walk."

It took a bit of convincing myself, but eventually I became confident that it did not mean that they were each walking at the same rate as each other after their lunch meeting.

But even then, I struggled with figuring out how I arrived at 6AM.

I like the method of switching to the 24 hour clock (as opposed to the AM/PM clock), and setting their arrival times as 16:00 and 21:00, with their meeting at 1200, then solving it.

[11235813213455]

just summing it up, v{i} are ladies speeds:

    MA = v1*x = v2*9
    MB = v1*4 = v2*x
    → v1 = 9*v2/x
    → 9*4*v2/x = v2*x
    → x = 6