One morning it begins snowing heavily, and continues snowing at a constant rate. At noon a snowplow starts down a long road, clearing the snow as it goes. At 1:00 a second plow starts at the same place and follows the first plow, clearing the snow that has fallen since the first plow passed. At 2:00 the second plow catches up to the first. When did it start snowing?

no way to know.

How much snow was on the ground?
So far, all we know is that it started snowing some time before noon.