## 141. Math Puzzle $2 / 77$

A KAP wants to deliver grain to the collection point by 11:00 AM. If she takes the tractor, the load would only arrive at 11:30 AM. If she takes the truck, it would already be there by 10:45 AM.

How far is the collection point, if both vehicles start at the same departure time, the tractor averages $15 \mathrm{~km} / \mathrm{h}$, and the truck $30 \mathrm{~km} / \mathrm{h}$?
The registration point is $x \mathrm{~km}$ away. The departure time of the two vehicles is $t$ o'clock. The hours are divided decimally in the solution:

Tractor: $15 \cdot(11.50-t)=x$

Truck: $30 \cdot(10.75-t)=x$

from this it follows: $t=10$. Distance $x=22.5 \mathrm{~km}$.