Answer:
300 mph
Step-by-step explanation:
Let's say x is the speed of the plane in still weather.
The time it takes flying against the wind is:
990 mi / (x − 30 mph)
The time it takes flying with the wind is:
990 mi / (x + 30 mph)
The total time is 6⅔ hours, so:
6⅔ hr = 990 mi / (x − 30 mph) + 990 mi / (x + 30 mph)
6⅔ = 990 / (x − 30) + 990 / (x + 30)
20/3 = 990 / (x − 30) + 990 / (x + 30)
Solving this equation for x, multiply both sides by 3 (x − 30) (x + 30):
20 (x − 30) (x + 30) = 2970 (x + 30) + 2970 (x − 30)
20 (x² − 900) = 2970x + 8910 + 2970x − 8910
20x² − 18000 = 5940x
20x² − 5940x − 18000 = 0
x² − 297x − 900 = 0
Factor:
(x − 300) (x + 3) = 0
x = 300 or -3
Since x must be positive, x = 300 mph.
