An airplane travels 3295 kilometers against the wind in 5 hours and 4095 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
Let's represent the rate of the plane in still air as "p" and the rate of the wind as "w".
Against the wind:
Distance = Rate × Time
3295 = (p - w) × 5
With the wind:
Distance = Rate × Time
4095 = (p + w) × 5
We now have a system of two equations:
1) 3295 = (p - w) × 5
2) 4095 = (p + w) × 5
First, we can simplify both equations by dividing both sides by 5:
1) 659 = p - w
2) 819 = p + w
Next, we can add the two equations together to eliminate w:
659 + 819 = 2p
1478 = 2p
Now divide both sides by 2 to solve for p:
p = 1478 / 2
p = 739
The rate of the plane in still air is 739 km/h.
To find the rate of the wind, we can substitute the value of p into one of the original equations. Let's use the first one:
659 = 739 - w
Now solve for w:
w = 739 - 659
w = 80
The rate of the wind is 80 km/h.
Therefore, the rate of the plane in still air is 739 km/h and the rate of the wind is 80 km/h.