It takes 2 hours longer to fly between New York and Los Angeles against the wind versus flying with the wind... (description)

Question

It takes 2 hours longer to fly between New York and Los Angeles against the wind versus flying with the wind. The distance between John F. Kennedy International Airport and Los Angeles International Airport is about 2500 miles. Let x be the airspeed of a jet. The wind speed is 100 miles per hour. Because of the wind, it takes longer to fly one way than the other. Find the speed of the jet.

Answer 1

Distance = rate * time

Distance/rate = t

2500/(x+100) + 2 = 2500/(x-100)

2500(x-100) + 2(x+100)(x-100) = 2500(x+100)

2500x - 250000 +2(x^2 - 10000) = 2500(x+ 100)

2500x - 250000 + 2x^2 - 20000 = 2500x + 250000

2500x + 2x^2 - 270000 = 2500x + 250000

2x^2 - 270000 = 250000

2x^2 = 250000 + 270000

2x^2 = 520000

x^2 = 260000

x is about 510

2500 miles at 610 mph = 4.1 hours

2500 miles at 410 = 6.1 hours