Question 299199: An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed?
Found 3 solutions by mananth, MathTherapy, Alan3354:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed?
let rate of plane in still air be x
let rate of wind be y
(x-y)*4 =1200
(x+y)*3=1200
4x-4y=1200
3x+3y=1200
3(4x-4y)+4(3x+3y)=3*1200+4*1200
12x-12y + 12x +12y = 8400
24x=8400
x=350 mph rate of plane in still air
(x+y)*3=1200
(350+y)*3 =1200
1050+3y=1200
3y=1200-1050
3y= 150
y=50 mph rate of wind
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed?
Let the plane's speed be S, and the wind's speed W
Since it took 4 hours against a headwind to fly 1,200 miles, then speed =  or 300 mph.
This means that the speed of the plane - windspeed = 300 mph, or, S - W = 300
Since it took 3 hours with the headwind to fly 1,200 miles, then speed =  or 400 mph.
This means that the speed of the plane + windspeed = 400 mph, or, S + W = 400
S - W = 300 ------ (i)
S + W = 400 ------ (ii)
2S = 700 ------- Adding eqs (i) & (ii)
S, or speed of plane =  or  mph
Substituting 350 for S in eq (i), we get:
350 - W = 300
- W = - 50
W, or windspeed =  or  mph
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! An airplane took 4 hours to fly 1200 miles agianst a headwind.The return trip with the wind took 3 hours. Find the speed of the plane in still air and the speed of the wind. What is the speed of the wind in still air? What is the wind speed?
----------------
1200/4 = 300 mph groundspeed
1200/3 = 400 mph groundspeed
The plane's airspeed is the average, = 350 mph
----------------
The windspeed is the difference, = 50 mph
|
|
|
