1. A car is driving at a constant speed in one direction along a straight road, near which there are two houses. At noon, when the car had not yet reached the houses, the sum of the distances from it to these houses was 10 km. After 10 minutes, when the car had already passed both houses, it turned out that the sum of the distances from it to the houses was again 10 km. What is the speed of the car? (Problem author - I. Rubanov)
Answer: 60 km/h. Solution: Let the houses be at points $A$ and $B$, the car was at point $C$ at noon, and at point $D$ 10 minutes later (see figure). According to the problem, $C A + C B = D A + D B = 10$. Note that $C A + C B = 2 C A + A B$, and $D A + D B = 2 D B + A B$, from which we get $C A = D B$. 

![](https://cdn.mathpix.com/cropped/2024_05_06_09d278345392f24661f8g-1.jpg?height=71&width=386&top_left_y=547&top_left_x=1509)
Therefore, $C D = C A + A B + B D = 2 C A + A B = 10$ km. This means that in 10 minutes, the car traveled 10 kilometers. Therefore, in 60 minutes, it will travel 60 km.