Not really a performance question… well kind of……
I’m flying along with a tailwind… what would I do to my airspeed if I wanted to ….
Fly for max endurance
Fly for max range.

I’m flying along with a tailwind… what would I do to my airspeed if I wanted to ….
Fly for max endurance
Fly for max range.

That's covered pretty simply in Bob's book -

Range - compared to the nil wind case, increase speed a little in a headwind, reduce speed a little in a tailwind so that SGR is maximised. Usually, we don't worry too much in a tailwind and often just go for maximum SAR.

Endurance - is not interested in wind so we just go for minimum fuel flow.