This Is NOT A Trick Question. The Famous Snowplow Math Problem

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[CJBrunt]

And like any math problem, this relationship between speed and depth only holds true for spherical snowplows operating in a vacuum.

[cisium]

The key to all of these "seemingly impossible problems" is always the same: assume something you haven't been given any indication you can assume. In other words, go to the point where critical thought and deductive reasoning diverge, and choose deductive reasoning merely because it enables you to answer the problem.

[shanedk]

If the speed of the plow is inversely proportional to the height of the snow, wouldn't that mean that when there's no snow the plow can go infinitely fast? That doesn't seem like good reasoning to me.

[anatomicallymodernhuman]

Before the snow begins to stick, you can either solve for the plow’s velocity or location, but not both at once. Either way, the key assumption is that the driver has a cat which is both alive and dead at the same time.

[GrahamSiggins]

Anybody else super annoyed by them saying this is "not a trick question" but then the very first and very necessary step to solving this is to make this assumption about the speed of the snowplow being inversely proportional to the rate the snow falls?

[anthonykf]

pfft, easy. The horses name was Friday.

[binkbonkie]

i was just gonna be like "it started in the morning"

[SimplyChrist]

It started snowing at 11:59 a.m. At 12:59 p.m., the snowplow driver suddenly discovered he was getting paid by the hour....

[jgallantyt]

At first I was thinking the same thing about the inverse relationship between snow and speed, but I discarded it because that's not how snow plows work. They don't approach infinite speed as the depth of snow approaches zero. Also they generally go the same speed until you hit extreme amounts of snow. For those reasons I discarded the idea that it was inversely related and then couldn't solve it.

[MWSin]

It's a well known fact that snowplows travel at infinite speed on clean roads, and exist simultaneously at all points in space (except those that have snow).

[marvinkitfox]

"A snowplow started out at noon, going 2 miles in the first hour and 1 mile in the second hour. What time did it start snowing?"
The snowplow is very unlikely to start snowing, thank you. Smoking, maybe.. But snowing? hardly likely.

[Dwatthaell]

I never learned calculus, but I do happen to drive a snowplow. I'll freely admit, this math hurts my head. However, from a snowplow operations standpoint, the answer is not what the calculus provides. Even if we assume there's no road pre-treatment occurring, which there would be, but just for simplicity's sake.. The snowplow driver would have been called out a few hours in advance, and would have begun plowing when the snow started to fall.

You start plowing a route in those conditions as soon as you can. It saves a small amount of load stress on your plow, and makes the job easier over the long run. *chuckles*

[gcree]

The snow plough's speed decreasing as the amount of snow on the road increases doesn't mean that those 2 quantities are inversely proportional. As many people have pointed out, such a relationship would not satisfy the boundary condition when there is no snow on the road. If the writers of the question expected people to make the assumption that was made in this video then this is a bad question for multiple reasons.

[SylviusTheMad]

The assumption that the speed of the snowplow is inversely proportional to the height of the snow is demonstrably false. However, the plow's loss of speed from its maximum speed (which is finite) can be proportional to snow depth.

Simply assuming the speed is inversely proportional to the snow depth creates a model in which the plow travels at infinite speeds when there isn't any snow.

[Toshinben]

If this plow only covers 3 miles in 2 hours, why does the driver still have a job?

[frognik]

Now I'm assuming that the snow fall was constant and the plow only went 1 mile in the 2nd hour because it ran out of fuel.
You know, since we're assuming things.

[miallo]

I had a different assumption for the speed of the plow: It is going at a constant speed but they had 30min lunchtime at 1pm. But maybe that was just too realistic...

[hcnuup]

"What time it did start snowing?" Well if it snows at such a rate that within hours snowplows basically go to a standstill, presumably due to being completely buried, it started snowing when God decided it was time to wipe out humanity.

[mindofmadness]

Stuff like this is why I became a Photographer.

[Chew]

If you live in Danville, Illinois the snow plows won’t plow your street until two days after it starts snowing.