SOLUTION: An airplane is flying into a headwind travels the 1800 mi flying distance between New York and Albuquerque, NM in 3 hours 36 min. On the return flight, the same distance is travele

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: An airplane is flying into a headwind travels the 1800 mi flying distance between New York and Albuquerque, NM in 3 hours 36 min. On the return flight, the same distance is travele      Log On


   

Question 725849: An airplane is flying into a headwind travels the 1800 mi flying distance between New York and Albuquerque, NM in 3 hours 36 min. On the return flight, the same distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind assuming that both remain constant.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
An airplane is flying into a headwind travels the 1800 mi flying distance between New York and Albuquerque, NM in 3 hours 36 min. On the return flight, the same distance is traveled in 3 hours. Find the airspeed of the plane and the speed of the wind assuming that both remain constant.
***
let x=airspeed of the plane or speed of plane in still air
let c=speed of the wind
(x+c)=speed of plane in downwind
(x-c)=speed of plane in headwind
Travel time=distance/speed
3 hrs and 36 min=3.6 hrs
..
1800/(x-c)=3.6
1800/(x+c)=3
..
1800=3.6x-3.6c
1800=3x+3c
..
5400=10.8x-10.8c
6480=10.8x+10.8c
add
11880=21.6x
x=550
3c=1800-3x=150
c=50
airspeed of plane=550 mph
speed of the wind=50 mph