1. A straight road passes not far from Mount Fuji. The driver of a car noticed the mountain 60 km to the north, and an hour later - 45 km to the west. What is the shortest distance the car passed from Mount Fuji?
Answer: 36 km.

Solution: The mountain and the observation points are at the vertices of a right-angled triangle with legs of 60 and 45. The hypotenuse in this case is 75. By equating the areas of the triangle calculated in different ways, we get that the product of the legs is equal to the product of the hypotenuse and the height, which is the required distance.

Thus, $60 \cdot 45=75 \cdot x \Rightarrow x=36$.

Grading criteria. Only the answer - 1 point. Answer with a diagram of the right-angled triangle and the height - 2 points.