How do I work this problem? Flying with the wind, an airplane can travel 1080 miles in six hours, but against the wind, it goes 360 miles in half the time. Find the air speed and wind speed
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To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the speed of the airplane in still air is A miles per hour, and the speed of the wind is W miles per hour.
When the airplane flies with the wind, its effective speed is increased by the speed of the wind. So, the speed becomes (A + W) miles per hour.
Given that the airplane can travel 1080 miles in 6 hours, we can set up the equation:
(A + W) * 6 = 1080
Simplifying this equation, we get:
6A + 6W = 1080
Similarly, when the airplane flies against the wind, its effective speed is decreased by the speed of the wind. So, the speed becomes (A - W) miles per hour.
Given that the airplane can travel 360 miles in half the time, which is 6/2 = 3 hours, we can set up the equation:
(A - W) * 3 = 360
Simplifying this equation, we get:
3A - 3W = 360
Now, we have a system of equations:
6A + 6W = 1080
3A - 3W = 360
To find the values of A (air speed) and W (wind speed), we can solve this system of equations using any suitable method, such as elimination or substitution.
Let's solve the system using the elimination method.
First, we'll multiply the second equation by 2 to make it easier to eliminate the W terms:
6A + 6W = 1080
6A - 6W = 720
Now, we can add the two equations to eliminate the W terms:
(6A + 6W) + (6A - 6W) = 1080 + 720
Simplifying, we get:
12A = 1800
Dividing both sides of the equation by 12, we find:
A = 150
Now, we can substitute this value back into one of the original equations to find W.
Let's substitute it into the first equation:
6(150) + 6W = 1080
Simplifying, we get:
900 + 6W = 1080
Subtracting 900 from both sides, we find:
6W = 180
Dividing both sides by 6, we find:
W = 30
Therefore, the air speed (A) is 150 miles per hour and the wind speed (W) is 30 miles per hour.
plane's normal speed = s
wind speed = w
1080(s+w) = 6
360/(s-w) = 3
6s + 6w = 1080
3s - 3w = 360
12s = 1800
s = 150
w = 30