Let C be the point where they meet in the middle and s be dawn.
It takes Lady 1 `12 - s` time to walk AC and 4 time to walk BC. It takes Lady 2 `12 - s` time to walk BC and 9 time to walk AC.
Let's find the ratio of time it takes Lady1 to walk a distance to time it takes Lady2 to walk a distance. The ratio should be the same for all distances since their speed doesn't change.
Thus, (12-s)/9 = 4/(12-s) <=> s^2 -24s + 108 = 0.
The quadratic formula gives us s = 6, 18. Since 0 <= s < 12, s = 6.
It takes Lady 1 `12 - s` time to walk AC and 4 time to walk BC. It takes Lady 2 `12 - s` time to walk BC and 9 time to walk AC.
Let's find the ratio of time it takes Lady1 to walk a distance to time it takes Lady2 to walk a distance. The ratio should be the same for all distances since their speed doesn't change.
Thus, (12-s)/9 = 4/(12-s) <=> s^2 -24s + 108 = 0. The quadratic formula gives us s = 6, 18. Since 0 <= s < 12, s = 6.