Answer:
The speed of the wind is 40mph, the speed of the plane in still air is 360mph
Step-by-step explanation:
distance = speed * time
Both legs of the trip are 800 miles, let 'x' represent the speed of the plane in still air and 'w' represent the speed of the wind, then 'x+w' represents the speed with the wind and 'x-w' represents the speed into the wind
800 = (x-w)2.5
800 = (x+w)2
Rewrite equations:
800=−2.5w+2.5x;800=2w+2x
Steps: Solve 800=−2.5w+2.5x for w:
800=−2.5w+2.5x
800+2.5w=−2.5w+2.5x+2.5w(Add 2.5w to both sides)
2.5w+800=2.5x
2.5w+800+−800=2.5x+−800(Add -800 to both sides)
2.5w=2.5x−800
2.5w/2.5 = 2.5x - 800 / 2.5 (Divide both sides by 2.5)
w=x−320
Step: Substitute x−320 for w in 800=2w+2x:
800=2w+2x
800=2(x−320)+2x
800=4x−640(Simplify both sides of the equation)
800+−4x=4x−640+−4x(Add -4x to both sides)
−4x+800=−640
−4x+800+−800=−640+−800(Add -800 to both sides)
−4x=−1440
-4x/-4 = -1440/-4 (Divide both sides by -4)
x=360
Step: Substitute 360 for x in w=x−320:
w=x−320
w=360−320
w=40(Simplify both sides of the equation)
solving this system we have:
w=40
x=360
Therefore, the speed of the wind is 40mph, the speed of the plain in still air is 360mph
