If a plane can travel 510 miles per hour with the wind and 410 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air

(510 + 410) / 2 = 460 mi/hr

510mph - x = 410mph + x |speeds equal taking the wind out of play

100 = 2x

x = 50mph

Speed of plane in still air = 460mph (410mph + 50mph)

It's the average, (510 + 410) / 2 = 460 mi/hr, and it's called airspeed, not "the speed in still air."