Does a powered aircraft fly faster when in a head wind or with a trailing wind? The question revolves around the head wind should provide 'better' lift, and trailing winds have very little to 'push' against.
A tailwind provides a faster groundspeed.
The aircraft moves through the air so whether the ground is moving relative to the mass of air has no relevance to the aerodynamics of an aircraft at cruising altitude.
a British Airways passenger jet approached supersonic speed this week as it rode a surging jet stream from New York to London.
They mean groundspeed - so the term supersonic is moot.
The Boeing 777-200 jet reached a ground speed of 745mph as it rode winds of more than 200mph across the Atlantic. At ground level, the speed of sound is 761mph.
Aircraft often use the predominantly westerly† jetstream when flying from the USA to Europe, From Japan to California or across the USA. Flying the other way they pick an altitude to avoid it. Wikipedia
The Jetstream is a high speed, high altitude, wind that blows moderately reliably in one direction.
† Westerly means "blowing from the west" - towards the east.
Headwind is good for take-off and landing. It adds extra speed for free at the start of the take-off run, rsp. allows to come in slower for landing, reducing the landing distance.
Tailwind is good for enroute flight. It pushes the aircraft forward and adds extra miles per hour for free. The speed relative to the surrounding air is the same at the same power setting and altitude regardless of wind speed, but when measured relative to the ground the wind speed must be added to the air speed.
But on the way back from a tailwind leg the aircraft has to fly in a headwind, and the added time and fuel expense is higher for the sum of both trips in comparison to trips made when no wind is blowing. Why? Let's assume the aircraft will fly at the same power setting, and will achieve 200 mph in still air. The trip to a destination 1000 miles away will take 1000 / 200 = 5 hours in still wind for a roundtrip time of 10 hours.
Now add to that a 50 mph tailwind, and the trip will take 1000 / 250 = 4 hours. On the return trip we need to subtract the wind: Now it will take 1000 / 150 = 6 hours 40 min to fly back. The total flight time with wind is 10 hours 40 min, and those 40 min of longer flight time consume proportionally more fuel and crew time.
Tailwind is only good when you don't plan to return, or when the wind will have changed when you go back.
Constant wind does not affect the lift or drag of an aircraft.
As stated by others, you will travel faster in relation to the ground with tailwind but your airspeed will stay the same no matter what wind you have.
Shortly after you are in the air, the aircraft travels with the wind, rather then with the surface of the earth. The aircraft wouldn't notice any wind. For an airborne aircraft, the air always stands still. Wind is only the movement of air in relation to the ground, and the aircraft doesn't relate to the ground once it is airborne.
If you are having tailwind, the aircraft will travel with the same speed through the air, but with an increased speed over the ground. This is why you take off into the wind: Your airspeed (the speed the aircraft travels through the air, so the sum of windspeed and groundspeed) is higher with a lower ground speed.
Here the maths: Let's say you have 10kt headwind and you are standing at the runway. When standing still your airspeed is already 10kt eventhough your groundspeed is 0kt. As you start moving, the airspeed will always be 10kt more then your groundspeed.
Conclusion: The wind doesn't make an airplane faster in relation to the air, but in relation to the ground the wind can change the speed of an aircraft, but not by producing more lift/drag, but by simply moving the aircraft along in the air.
The question actually has nothing to do with aerodynamics. It's a matter of relative motion, which is traditionally considered physics, but IMO is really nothing more than simple vector arithmetic.
Consider this equivalent question:
Before you board your airplane, you walk through an airport. You approach two parallel "pedestrian conveyor belts," one moving away from you and one moving toward you. Which one should you walk across if you want to get to the other side faster?
Now replace your body with the airplane, and the conveyor belts with "wind" (moving masses of air). Does that make it more clear?
When looking at the physics, the speed of an aircraft is the speed relative to the air. For this, it is not relevant how the air moves relative to the Earth - or any other planet, for that matter.
The aircraft does not even "know" the direction of wind.
So there can not be a difference in the aerodynamics, in a very fundamental way.
If you ask about the speed relative to the ground, you can just add the vectors of both speeds.