<em>Speed of the airplane for the wind is 583 mph and speed of the airplane against the wind is 517 mph</em>
Given that the speed in still air is 550mph, then we can say that
speed for the wind = 550 + w
speed against the wind = 550 - w
Considering that it travels 3498 miles for the wind and 3102 against the wind, we can then say that
3498/(550+w) = 3102/(550-w)
if we cross multiply, we have
3498 × (550-w) = 3102 × (550+w)
1923900 - 3498w = 1706100 + 3102w
<em>collecting like terms</em>
1923900 - 1706100 = 3102w + 3498w
217800 = 660w
w = 217800/660
w = 33
If w = 33, then the speed for and against the wind is 550+33 = 583 mph and 550 - 33 = 517 mph respectively.
read more here; brainly.com/question/11221202