The Simple Flying Question That Everyone Gets Wrong

#VeritasiumContest
This video was made as a submission to the Veritasium SciComm Contest, but even if you're not here for that, I hope you have found this interesting, and perhaps learnt something new.
This is my first foray into video production, but it's been a blast, and I hope to do more.
Thank you Derek, Emily, and everyone at Veritasium for this chance to engage with science education in an entirely new way, and for all that you do for the community at large.
Cam
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[@electrodacus]

You are assuming plane uses all engine power in the non windy day so there is no extra power left to compensate for the wind. It is also unrealistic to think you get wind speeds equal or even close to typical airplane speeds.
I think most students did answered correctly to this question or your question was badly formulated.

[@patrickcleburneuczjsxpmp9558]

You do understand, however, that traveling half a given distance at a speed X+Y mph (where X and Y are both greater than O) and half that distance at X-Y mph will take longer than traveling the full distance at X mph?

[@electrodacus]

​@@patrickcleburneuczjsxpmp9558 I do not think you understood my comment. A plane can and will fly at order of magnitude higher speed than wind speed and even in this example the wind speed was just 25% of plane speed. So assuming plane has sufficient power it will fly at same speed in windy day as it will fly in a day with no wind.
There is no imposed limitation for the aircraft power thus it can maintain same speed even with a headwind. The fuel consumption will be affected but not the speed relative to ground.

[@TheRandomTandem]

Thanks for really taking the time to think about, and engage with this question, but I'm afraid you've misunderstood a couple of the main points I was making.
First, this question is about speed, not about engine power.
200 knots is 200 knots, regardless of what quantity of power is applied.
As you imply, on windy days aircraft may increase power, and thus increase airspeed when facing a headwind, but this question is not about that.
It's testing your understanding of how changes of speed affect time, it's not about the practical considerations of flying in windy conditions.
Second, yes it is unrealistic to expect wind to travel near the velocity of an aircraft, but the video addresses this.
I start with a realistic wind speed that is one quarter of the aircraft's airspeed, but when the answer is not intuitive, taking values to the extreme is often a good way of demonstrating the effect of its change.
For example, if you wanted to understand how a planet's mass affects an object that orbits it, you could calculate what would happen if its mass were doubled, or halved.
Realistic? No.
Insightful? Absolutely.
I stand by every word in this video, and am confident in its validity as an insightful tool for learning.

[@electrodacus]

@@TheRandomTandem I think you will need to define aircraft speed. If aircraft speed is relative to ground and that is also what the aircraft measures then wind speed and direction will not impact the aircraft. What likely majority of your students do not know is that aircrafts measures speed relative to air speed and not relative to ground (as it is the case for a vehicle/car).
So you can control the speed of an aeroplane based on GPS thus flying at constant 200kt relative to ground in both direction even with a 50kt wind. Of course it will use significantly more fuel in one direction than the other but it can maintain constant average speed relative to ground.
I will say that you need to mention in the problem that airplane speed is measured relative to air not relative to ground.

[@TheRandomTandem]

​@@electrodacus In reference to the video, there is one point where I use the word 'speed' in relation to the aircraft, and in doing so, I say 'airspeed', which is the speed at which it passes through the air surrounding it.
Defining Airspeed and Groundspeed is not necessary for people watching this, as it does not deal with how aircraft measure speed, or maintain speed.
This isn't about practical flying considerations, and my assumption is that people intuitively understand that planes move faster over the ground in a tailwind, and slower over the ground in a headwind. That's it. I just wanted to get a single surprising concept across, not get into how real world aircraft can negate the adverse affects of wind.
The majority (in fact all) of my students do understand how aircraft measure speed, as I teach aviation at a University.
I will concede that the text on the right of screen could say 'Aircraft Airspeed 200kts' instead of 'Aircraft 200kts' to avoid ambiguity.
Also, if I was to make this video purely for my own interest, I would cover this point, as well as a few others.
However this was made for a video competition with a maximum length allowance of one minute, so the script was kept to a bare minimum.