The Snowplow Problem Revisited 1

The Snowplow Problem Revisited
Author: Xu, Xiao-peng
College Mathematics Journal, Vol. 22, no. 2, p. 139, 1991.

A famous problem in elementary differential equations is the snowplow problem:
“One day it started snowing at a steady and heavy rate. A snowplow got started at noon, went 2 miles in the first hour, and 1 mile in the second. What time did it start snowing?”
Usually this problem is solved by setting t=0 to be noon and setting up a differential equation, solving it, and then using the information to eliminate the irrelevant constants to find t_0. This method involves a tedious amount of algebra, so Xu offers a clever and simple calculus trick to get an equation for t_0 that is much easier to solve. (Summary by Ellen Le, Pomona College '10)

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