Answer:
The speed of the plane in still air is 590 mph
The speed of the wind is 20 mph
Step-by-step explanation:
Let's call:
x = Speed of the plane in still air
y = Speed of the wind
The plane traveled d=4575 miles with the wind in t=7.5 h. The speed calculated with this data corresponds to the sum of the speed of the plane and the speed of the wind, thus:
[tex]\displaystyle x+y=\frac{4575}{7.5}=610[/tex]
x + y = 610 [1]
The plane traveled 4275 miles in 7.5 hours against the wind, thus the speed calculated is x - y:
[tex]\displaystyle x-y=\frac{4275}{7.5}=570[/tex]
x - y = 570 [2]
Adding [1] and [2]:
2x = 610 + 570 = 1180
x = 1180 / 2 = 590
From [1]:
y = 610 - 590 = 20
The speed of the plane in still air is 590 mph
The speed of the wind is 20 mph
