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Jet-streams are high-altitude winds which flow from west to east. They can be provide a very strong tailwind or headwind depending on which direction the aircraft is going.
What is the historic record of the strongest jet-stream ever countered by commercial aircraft? I'd expect the result to be either a very short east-going flight (much shorter than the expected time of travel), or a very long west-going flight.
Jetstreams generally don't stay perfectly straight. They tend to follow a meandering, curved path so it would be rare for a flight to stay in the max tailwind for very long.
Dispatchers will often take advantage of jetstreams and plan the routing to follow part of the jetstream core.
There is a website called Ground Speed Records where pilots can post photos of high groundspeeds for an "Unofficial" record.
Here is an example from that website giving a groundspeed of 736 knots from a 240 knot jetstream tailwind. That is probably about the highest jetstream speed you will see: B747-400 Ground Speed Records
This is an answer to I'd expect the result to be either a very short east-going flight (much shorter than the expected time of travel), or a very long west-going flight.
Air India Flight 173 is probably the best example for this. The flight now travels over Pacific Ocean, enroute from New Delhi to San Francisco. This is opposite to flying over great circle route, but inspite of that Air India reduced the flying time by 2 hours because of jetstreams. Now, the total distance travelled could be anything from 9,300-10,000 miles, and the flight covers it in less than 15 hours.
On October 21, AI 173 flew 10,080 miles in 15.25 hours. Flightaware.
Here is a small video on AI 173, that I have made.
