Answer:Wind speed = 30 miles/hour
Plane speed = 450 miles/hour
Step-by-step explanation:
First we have to know the formula for finding speed, which is distance divided by time
Speed = distance/time
Then we label the speed of the plane to be x
And the spend of the wind to be y
From the question, we are told that when the plane flies into the wind, it takes 4 hours to travel a distance of 1680 so we have the time and distance
And since the plane is flying against the wind speed
We can form an equation
x - y = 1680/4
x - y = 420 (1)
Then when the plane is coming back, the wind is going in the same direction with the plane and it take 3.5 hours to cover the same 1680 miles distance, so we form another equation
x + y = 1680/3.5
x + y = 480 (2)
So we solve (1) and (2) simultaneously
x - y = 420 (1)
x + y = 480 (2)
Using elimination method, we eliminate y by adding both equations
2x = 900
x = 450 miles/hour
So therefore, plane speed is 450 miles/hour
Putting the answer in either (1) or (2) to get y
I choose to put it in (2)
x + y = 480
450 + y = 480
y = 480 - 450
y = 30 miles/hour
So therefore, wind speed = 30miles/hour
