## 19. Picnic

At nine o'clock in the morning, Paul set off on his bicycle from point $A$ to point $B$ at a speed of $15 \mathrm{km} /$ h. At a quarter to ten, Pierre in turn set off from $B$ to $A$ at a speed of 20 km/h. They agreed to have a picnic halfway and strictly adhered to this condition. At what time did they meet?
19. Let $x$ be half the distance from $A$ to $B$. Then the time Paul spent traveling from $A$ to the meeting point is $x / 15$. The time it took Pierre to cover the same distance is $x / 20$. But since Pierre left three-quarters of an hour later, then

$$
x / 15 = x / 20 + 0.75
$$

and, therefore, $x = 45$.

Thus, Paul traveled to the meeting point for 3 hours, and the friends met at noon.