Find the speed of the plane with no wind and the windspeed.

Question

It took an airplane 4hours to fly 1,600mi against a headwind. The return trip with the wind took 313hours. Find the speed of the plane with no wind and the windspeed.

Answer 1

While I can't give an exact answer with the info given, I can show how to solve once the correct time for the return trip is known. Let x be the airplane speed, y be the wind speed and assume 3 hours for the return trip.

 

Going against the wind: 4(x-y) = 1600

Going with the wind: 3(x+y) =  1600

Therefore 4x - 4y = 3x + 3y

4x = 3x + 7y

x = 7y

 

3x + 3y = 1600

21y + 3y = 1600

24y = 1600

y = 66 2/3

x = 7y = 466 2/3