The jet stream may work for (tailwind) or against a plane (headwind). As you say that means a plane can fly 120 knots faster in a tailwind and 120 knots slower in a headwind. Similar to going along with the current in a river or against the current in a river.
The gains or losses depend on the current strength of the jet stream, the direction of travel, and the distance of travel.
Flying high (cruising altitude above 30,000 ft) means thinner air and more efficient flying at cruising altitude where jets are designed to be most efficient.
Additional advantages to flying at high altitudes: it’s above the clouds usually, less weather-related turbulence, and it takes a long time to glide down, giving pilots more options in emergency situations.
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