03-18-2021, 03:24 PM
Quote:One day it started snowing at a heavy and steady rate. A snowplow started out at noon, going 2 miles the first hour and 1 mile the second hour. What time did it start snowing?
Eventually, I was able to solve this with high school calculus and a little algebra. But it should also be soluble by a bit of programming, perhaps by simulation, or by successive approximation, or perhaps even using SOLVE. Perhaps there's a graphical or geometric approach.
via Bob (rprosperi) via a video via a defunct blog via a 1942 textbook
The blog said (mild spoiler):
Quote:Despite being drawn from a text on the lofty subject of differential equations, this problem should be solvable by anyone who has had college-level Calculus I, or a year of high school calculus. The hardest part of the problem is not the math required to solve it, but the fact that you must make some assumption on your own about the relationship between snow and plowing speed. That is, how does the speed of a snowplow depend on the depth of the snow on the ground? The simplest reasonable assumption is this: The speed of a snowplow is inversely proportional to the depth of the snow it is plowing at each moment. Though it may be hard to believe, this assumption and the information given in the problem are enough to calculate a definite solution.
Back in college, I solved the homework problem for my mathematical modeling course by hand on paper using a little calculus, but I have often wondered how a student might approach the problem if they didn't know any calculus, but did have some ability to program. Many (if not all) “calculus problems” can be solved through fairly simple computer programming, and it turns out that this one is no exception.
(Personally, and for reasons of search, I would equally well call this the snowplough problem.)