
Differential Equations Ordinary and Partial Differential Equations Math Forum 
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April 6th, 2018, 09:41 PM  #1 
Senior Member Joined: Aug 2012 Posts: 2,045 Thanks: 584  The famous snowplow math problem
I saw this Youtube video today. It's a really striking puzzle. I confess to not taking the trouble to follow each step myself, but differential equations fans will really enjoy this. Here is the problem. One day it started snowing in the morning at a heavy and steady rate. A snow plow started out at noon, going 2 miles in the first hour and 1 mile in the second hour. What time did it start snowing? This is not a joke or a trick. It's a problem from a 1942 textbook on differential equations. It has a perfectly sensible solution using elementary calculus. Here's the vid. Last edited by Maschke; April 6th, 2018 at 09:47 PM. 
April 6th, 2018, 09:50 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,124 Thanks: 1102 
You left out a rather key point in your transcription. Snow removal is done at a constant rate. 
April 7th, 2018, 08:47 AM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 384 Thanks: 27 Math Focus: Number theory 
The Golden Mean!

April 7th, 2018, 08:56 AM  #4  
Senior Member Joined: Oct 2009 Posts: 555 Thanks: 179  Quote:
If you enjoy this do the following book: https://www.amazon.com/Differential.../dp/0070575401 It has this problem, and many similar cool ones.  
April 7th, 2018, 10:04 AM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra  
April 7th, 2018, 10:46 AM  #6  
Senior Member Joined: Sep 2015 From: USA Posts: 2,124 Thanks: 1102  Quote:
We are not amused.  

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famous, impossible, math, problem, puzzle, snowplow 
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