9.4. Along the shore of a circular lake with a perimeter of 1 km, two salmons are swimming - one at a constant speed of $500 \mathrm{m} /$ min clockwise, the other at a constant speed of 750 m/min counterclockwise. Along the edge of the shore, a bear is running, always moving along the shore at a speed of 200 m/min in the direction of the nearest salmon to it. How many full laps around the lake will the bear make in one hour?

ANSWER: 7.

CRITERIA

-/. For a specific initial position of the bear and the fish, direct calculations of their movements over the course of two or more laps of the bear around the lake are provided, followed by an explicit but unproven (though intuitively correct) statement that the average speed of the bear's rotation around the lake is approximately equal to that obtained in this numerical experiment. Based on this, the answer is obtained with an accuracy of $10 \%$.
Solution. Note that the bear runs to the nearest salmon if and only if it runs from a point on the shore that is equidistant from the salmons and not separated from the bear by the salmons. Since both points equidistant from the salmons move counterclockwise at a speed of $|750-500| / 2=125<200$ m/min, they will never catch up to the bear, and the bear will never be at such a point (except possibly at the initial moment). Since each of these points will run $125 \cdot 60$ meters in an hour, they will make exactly $125 \cdot 60 / 1000=15 / 2=7.5$ laps around the lake. Therefore, the bear, which never crosses either of these points, will make strictly more than 7 but strictly less than 8 laps, that is, 7 full laps.