A more serious question: I assume this kind of event doesn't actually save fuel because the airplane still has to maintain the same airspeed to avoid stalling, right?
If a plane maintains the same airspeed, but gets extra ground speed thanks to a tailwind, it'll complete its journey in less time and therefore should save fuel. (Unless it ends up having to circle the destination airport while it waits for its original landing slot!)
Of course, planes going the other direction will use extra, so overall we don't win.
Aren't some(all?) long-haul routes chosen on a flight by flight basis to take advantage of favourable winds where possible?
Compare yesterday's eastbound BA11 (LHR-Singapore) vs the westbound BA12 (Singapore-LHR) flights.[0] Neither route looks like a great circle.
Eastbound routing: London - north of Berlin - Minsk - Voronezh - Volgograd - cross Caspian sea - Turkmenistan - Lahore - New Delhi - KL - Singapore.
Westbound: Singapore - KL - south of Jaipur - Iran - just touched Turkmenistan - south of Baku - Tbilsi - Turkey (just) - south of Prague - south of Dortmund - LHR
[0] flightradar24.com or similar
It's even worse than not winning. You actually lose if you have to fly in the same wind both ways, once as a headwind and once as a tailwind. The extra time in the into the headwind direction is more than the time saved in the with a tailwind direction.
If the ground distance each way is D, airspeed is V, and wind speed relative to the ground is w, total time is D/(V-w) + D(V+w) = 2DV/(V^2-w^2) = 2D/(V-w^2/V).
For 0 < w < sqrt(V), this is more than the 0 wind case. (For w >= sqrt(V), the headwind is so high that you can't make any progress toward the destination).
If the ground distance each way is D, airspeed is V, and wind speed relative to the ground is w, total time is D/(V-w) + D/(V+w) = 2DV/(V^2-w^2) = 2D/((V^2-w^2)/V).
For 0 < w < V: this is more than the 0 wind case. For w >= V: the headwind is so high that you can't make any progress toward the destination).
The last result being somehow obvious ;)
The jetstream is small. You can avoid it and not have to pay extra. So yes, it can be an absolute win.
So yes it's a win, but a little more subtly.
2. For given airspeed, the plane flies less time with a tailwind than a headwind.
So, this does save fuel, I'd think.
Doing a little digging, it seems that there's also a significant risk of entering an overspeed condition during recovery, and inducing a structural failure! Makes sense considering that we're talking about speeds near Mach 1 to begin with.
It was in and out of the coffin corner before the pilots realized what was happening.
I watched a TV programme a couple of years ago talking about this on the U2 as the speeds were only a few knots apart and also varied with altitude and other factors.
The image at https://i.stack.imgur.com/Lu2Xt.jpg shows the airspeed corridor the pilots have to fly through. It's constantly flying on a knife edge.
So yes this does save fuel.
However, it's worth noting that if the outward (downwind) and return (upwind) legs are affected by the same wind, the outward savings are more than offset by the extra fuel needed for the return. Suppose the journey in your example is 200 miles. With no wind, that's an hour each way, so 2 hours total cruising time.
With the 100mph wind, the outward journey only takes 40 minutes (200 miles at 300mph), but the return takes 2 hours (200 miles at 100mph) for a total cruising time of 2:40, and a significantly greater total fuel burn.
(In practice, airlines may route the two legs quite differently to optimize better, taking advantage of the tailwind in one direction while avoiding it as much as possible when going the other way.)
Conclusion: increased wind increases the round trip time.
We're great at accidental terraforming now, we're actually warming the temperature of the planet.
But based on global reaction to the current terraforming I'm skeptical that we'll ever reach the point to where we can intentionally terraform the planet.