Math Is Fun Forum

John2017

Guest

The Snowplow Problem

Snow began falling sometime in the morning and conitnued to fall at a constant rate. At 8AM a snowplow was sent out. By 9Am the plow had traveled 20 miles, and by noon it had traveled an additional 20 miles. Assuming the speed of the plow is inversely proportional to the depth of the snow, when did the snow begin falling?

This is a basic DE that my teacher assigned due tomorrow. I'm having issues finding n (where n is the amount of time it snows before the snowplow comes through) in the equation p(t)=ln((t+n)/n), that I have previously derived hoping it may be correct. Any help is accepted thank you. (p(t) is the distance the snow plow travels and t is the time in hours)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Snowplow Problem

Hi;

Anything of use over here?

http://www.mathisfunforum.com/viewtopic … 77#p164877

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

john2017

Member

Registered: 2017-02-02

Posts: 2

Re: The Snowplow Problem

I looked at it and attempted to work through that problem. The n that I found was 30 minutes. However, when I went back to the equation to check its validity (plugging points back in) I found that the differential equation may not be exact for this problem.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: The Snowplow Problem

What DE did you get?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

john2017

Member

Registered: 2017-02-02

Posts: 2

Re: The Snowplow Problem

I got the same De of p(t)=ln((n+t)/n). But i may have just missed some sort of key word in the problem statement. I did try to follow that exact reasoning on that page and it left me with what I stated before