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April 6th, 2018, 09:41 PM   #1
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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.
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April 6th, 2018, 09:50 PM   #2
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You left out a rather key point in your transcription.

Snow removal is done at a constant rate.
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April 7th, 2018, 08:47 AM   #3
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The Golden Mean!
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April 7th, 2018, 08:56 AM   #4
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Quote:
Originally Posted by Maschke View Post
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.


If you enjoy this do the following book: https://www.amazon.com/Differential-.../dp/0070575401
It has this problem, and many similar cool ones.
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April 7th, 2018, 10:04 AM   #5
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Quote:
Originally Posted by Maschke View Post
I saw this Youtube video today. It's a really striking puzzle.
Me too, curiously. I had a bit of trouble forming my thoughts about the ploughs speed into an equation last night though.
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April 7th, 2018, 10:46 AM   #6
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Quote:
Originally Posted by Micrm@ss View Post
If you enjoy this do the following book: https://www.amazon.com/Differential-.../dp/0070575401
It has this problem, and many similar cool ones.
Ok. I see that in this version he just makes an arbitrary modelling assumption that is equivalent to the original problem's wording of constant removal rate.

We are not amused.
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