If a plane can travel 470 miles per hour with the wind and 430 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.
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Part 1
What is the speed of the wind?
Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".
Given that the plane can travel 470 miles per hour with the wind, we can write the equation:
p + w = 470
And given that the plane can travel 430 miles per hour against the wind, we can write the equation:
p - w = 430
To solve for the speed of the wind, we need to eliminate one of the variables. We can do this by adding the two equations together:
(p + w) + (p - w) = 470 + 430
2p = 900
Dividing both sides by 2, we get:
p = 450
Now that we have the speed of the plane in still air, we can substitute it back into one of the original equations to solve for the speed of the wind.
Using the equation p + w = 470:
450 + w = 470
Subtracting 450 from both sides:
w = 20
So the speed of the wind is 20 miles per hour.
Therefore, the speed of the plane in still air is 450 miles per hour.