[ Motion Problems ]

Two pedestrians set out at dawn. Each walked at a constant speed. One walked from $A$ to $B$, the other from $B$ to $A$. They met at noon and, without stopping, arrived: one - in $B$ at 4 PM, and the other - in $A$ at 9 PM. At what hour of the day was dawn?
After noon, the first pedestrian walked as much as the second did before noon.

## Solution

Let $x$ be the number of hours from dawn to noon. The first pedestrian walked $x$ hours before noon and 4 after, while the second walked $x$ hours before noon and 9 after. The ratio of the times is equal to the ratio of the lengths of the paths before and after the meeting point, so ${ }^{x} / 4=9 / x$. From this proportion, we find that $x=6$.

## Answer

At 6 a.m.