Some Mathematical Meandering III

In our last mathematical digression we studied the Snowplow Problem of Ralph Palmer Agnew, the solution of which using the logarithmic function appears on page 39 of his book Differential Equations (McGraw-Hill 1960).  Let us make the problem even more interesting following a suggestion by Murray S Klamkin that is given in Bender and Orszag's Advanced Mathematical Methods for Scientists and Engineers. Here is the Great Snowplow Chase.

One day it started snowing at a heavy and steady rate. Three identical snowplows started out at noon, 1 pm and 2 pm from the same place and all collided at the same time. What time did it start snowing?

11:30 AM