water of a very extensive cylindrical pond froze
Source: Spanish Mathematical Olympiad 1968 P1
December 4, 2022
algebra
Problem Statement
In one night the air temperature remained constant, several degrees below zero, and that of the water of a very extensive cylindrical pond, which formed a layer cm deep, it reached zero degrees, beginning then to form a layer of ice on the surface. Under these conditions it can be assumed that the thickness of the ice sheet formed is directly proportional to the square root of the time elapsed. At h, the thickness of the ice was cm and at h it was just over to freeze the water in the pond. Calculate at what time the ice sheet began to form, knowing that the density of the ice formed was .