## Poll

 I don't understand what's being asked. No votes (0%) Can't be solved with information given. No votes (0%) I don't know where to start. 1 vote (20%) You asked this one before, Wiz. 1 vote (20%) I know (explain) No votes (0%) Mr. Plow 1 vote (20%) Plow King 1 vote (20%) Total eclipse reminder 4-8-2024 3 votes (60%) I miss VegasGrinder. 2 votes (40%) I capitalize AM and PM. 1 vote (20%)

5 members have voted

Wizard Joined: Oct 14, 2009
• Posts: 23442
Thanks for this post from: July 25th, 2020 at 3:21:49 PM permalink
One morning it starts to snow at a constant rate. Later, at 6:00am, a snowplow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time, in other words its speed it inversely proportional to the depth of the snow. If the plow covered 10 miles from 6 to 7am and 5 miles from 7 to 8am, what time did it start snowing? It's not whether you win or lose; it's whether or not you had a good bet.
ThatDonGuy Joined: Jun 22, 2011
• Posts: 4959
July 25th, 2020 at 3:37:56 PM permalink

Let m be the number of minutes before 6 AM when it started snowing
The amount of snow cleared in the first 10 miles = 10m + 5 x 60
The amount of snow cleared in the next 5 miles = 5 (m + 60) + 5/2 x 60
10m + 300 = 5m + 300 + 150
m = 30, so it started snowing at 5:30 AM

ChesterDog Joined: Jul 26, 2010
• Posts: 972
July 25th, 2020 at 4:41:38 PM permalink
Quote: Wizard

...what time did it start snowing?...

that it started snowing at approximately 5:23 AM.
I see that the answer has something to do with the golden ratio--the snow started before 6:00 AM by one hour divided by the golden ratio.
Torghatten Joined: Feb 3, 2012
• Posts: 83
July 25th, 2020 at 4:46:19 PM permalink
Forgot way to much to solve it the intended way tonight...
But my excel-solution seems to converge towards (phi-1) hours before 6

So i guess it started 06:22:55

6:30 is for sure not correct
Wizard Joined: Oct 14, 2009
• Posts: 23442
July 25th, 2020 at 5:19:40 PM permalink
Quote: ChesterDog

that it started snowing at approximately 5:23 AM.
I see that the answer has something to do with the golden ratio--the snow started before 6:00 AM by one hour divided by the golden ratio.

I agree. Remember, for full credit you must show your work.
It's not whether you win or lose; it's whether or not you had a good bet.
Torghatten Joined: Feb 3, 2012
• Posts: 83
Thanks for this post from: July 25th, 2020 at 5:57:16 PM permalink

A try..

I assume it started to snow at time 0:

The plow have a speed at 1/X
so f(X) = 1/x

We have that the definite integral from x to (x+1) = 2 times the definite integral from (x+1) to (x+2)
The integral for 1/x = ln(x)

That gives:
ln(x+1) - ln(x) = 2*( ln(x+2) - ln(x+1) )
3*ln(x+1) -ln(x) = 2*ln(x+2)
3*ln(x+1) = 2*ln(x+2)+ln(x)
ln((x+1)^3) = ln(x) + ln((x+2)^2)
ln((x+1)^3) = ln((x+2)^2 * x)
ln(x^3+3x^2+3x+1)= ln(x^3+4x^2+4x)
x^3+3x^2+3x+1= x^3+4x^2+4x
x^2 +x-1 = 0

X = -1,618 and 0,618

As it started to snow before the plow started, the solution have to be positive and the answer is 0,618.

=it started to snow at 06:22:55

Sorry my poor english and formating.

DJTeddyBear Joined: Nov 2, 2009
• Posts: 10517
July 25th, 2020 at 7:34:30 PM permalink
Quote: Torghatten

Forgot way to much to solve it the intended way tonight...
But my excel-solution seems to converge towards (phi-1) hours before 6

So i guess it started 06:22:55

6:30 is for sure not correct

Quote: Torghatten

A try..

I assume it started to snow at time 0:

The plow have a speed at 1/X
so f(X) = 1/x

We have that the definite integral from x to (x+1) = 2 times the definite integral from (x+1) to (x+2)
The integral for 1/x = ln(x)

That gives:
ln(x+1) - ln(x) = 2*( ln(x+2) - ln(x+1) )
3*ln(x+1) -ln(x) = 2*ln(x+2)
3*ln(x+1) = 2*ln(x+2)+ln(x)
ln((x+1)^3) = ln(x) + ln((x+2)^2)
ln((x+1)^3) = ln((x+2)^2 * x)
ln(x^3+3x^2+3x+1)= ln(x^3+4x^2+4x)
x^3+3x^2+3x+1= x^3+4x^2+4x
x^2 +x-1 = 0

X = -1,618 and 0,618

As it started to snow before the plow started, the solution have to be positive and the answer is 0,618.

=it started to snow at 06:22:55

Sorry my poor english and formating.

Really? Twice you have him plowing BEFORE it starts snowing??? I think you missed a digit or something.

This math is was beyond my abilities, but I know that�s wrong.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ������������������������������������� Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
Wizard Joined: Oct 14, 2009
• Posts: 23442
Thanks for this post from: July 25th, 2020 at 8:19:16 PM permalink
Quote: Torghatten

A try..

I assume it started to snow at time 0:

The plow have a speed at 1/X
so f(X) = 1/x

We have that the definite integral from x to (x+1) = 2 times the definite integral from (x+1) to (x+2)
The integral for 1/x = ln(x)

That gives:
ln(x+1) - ln(x) = 2*( ln(x+2) - ln(x+1) )
3*ln(x+1) -ln(x) = 2*ln(x+2)
3*ln(x+1) = 2*ln(x+2)+ln(x)
ln((x+1)^3) = ln(x) + ln((x+2)^2)
ln((x+1)^3) = ln((x+2)^2 * x)
ln(x^3+3x^2+3x+1)= ln(x^3+4x^2+4x)
x^3+3x^2+3x+1= x^3+4x^2+4x
x^2 +x-1 = 0

X = -1,618 and 0,618

As it started to snow before the plow started, the solution have to be positive and the answer is 0,618.

=it started to snow at 06:22:55

Sorry my poor english and formating.

Great answer and solution Tor! I don't recall you being a member of the Beer Club yet, in which case welcome. This means I owe you a beer upon your next visit to Vegas.

To be perfectly honest, I asked this problem because I made a video going over the solution. This is my first math video in this kind of format so please go easy on me with your reviews.

It's not whether you win or lose; it's whether or not you had a good bet.
rsactuary Joined: Sep 6, 2014
• Posts: 1865
July 25th, 2020 at 10:02:24 PM permalink

Torghatten Joined: Feb 3, 2012
• Posts: 83
July 26th, 2020 at 6:12:47 AM permalink
Quote: DJTeddyBear

Really? Twice you have him plowing BEFORE it starts snowing??? I think you missed a digit or something.

This math is was beyond my abilities, but I know that�s wrong.

Quote: Wizard

Great answer and solution Tor! I don't recall you being a member of the Beer Club yet, in which case welcome. This means I owe you a beer upon your next visit to Vegas.

To be perfectly honest, I asked this problem because I made a video going over the solution. This is my first math video in this kind of format so please go easy on me with your reviews.