An airplane flying with the wind from Los Angeles to New York City takes 3.75 hours. Flying against the wind, the airplane takes 4.4 hours for the return trip. If the air distance between Los Angeles and New York is 2500 miles and the airplane speed and wind speed are constant, find the airplane speed and the wind speed.
+9665 Let x be the airplane speed and y be the wind speed.
Because distance/time = speed......
\(x+y=\dfrac{2500}{3.75}\)
\(x-y=\dfrac{2500}{4.4}\)
Add up the 2 equations:
\(2x=\dfrac{2500}{3.75}+\dfrac{2500}{4.4}=1234\dfrac{84}{99}\\ x = 617\dfrac{4}{9}\text{miles/h}\)
\(617\dfrac{4}{9}+y=\dfrac{2500}{3.75}\\ \dfrac{5557}{9}+y=\dfrac{2000}{3}\\ y = \dfrac{6000}{9}-\dfrac{5557}{9}=49\dfrac{2}{9}\text{miles/h}\)
The airplane's speed with the wind =2,500/3.75 =666 2/3 mph
The airplane's speed against the wind=2,500 / 4.4 =568 2/11 mph
The average speed of the plane coming and going:
[666 2/3 + 568 2/11] / 2 =617 14/33 mph
The average speed of the wind:
[666 2/3 - 568 2/11] / 2 =49 8/33 mph
