The snow plow problem

One day it started snowing in the morning at a heavy and steady rate. A snow plough started out at noon, going two miles in the first hour and one mile in the second hour. What time did it start to snow? Asssume that the snow plough's speed is inversely proportional to the amount of snow that has fallen: The more snow that falls, the lower the snow plough moves.

Hint: Obviously this requires a separable differential equation. A key is in the constants determined by initial conditions.