Answer:
The rate of the plane in still air (p) is 807 km/h, and the rate of the wind (w) is 80 km/h.
Step-by-step explanation:
To solve this problem, let's denote the rate of the plane in still air as 'p' and the rate of the wind as 'w'.
When the plane is flying against the wind, its effective speed is reduced by the speed of the wind. Therefore, the speed can be expressed as (p - w).
Similarly, when the plane is flying with the wind, its effective speed is increased by the speed of the wind, so the speed can be expressed as (p + w).
We have two pieces of information given in the problem:
Against the wind: The plane travels 4362 km in 6 hours, so we can set up the equation:
4362 = (p - w) * 6 ---> Equation 1
With the wind: The plane travels 5322 km in 6 hours, so we can set up another equation:
5322 = (p + w) * 6 ---> Equation 2
We now have a system of equations with two variables. We can solve this system to find the values of 'p' and 'w'.
To simplify the equations, divide both sides of Equation 1 by 6 and Equation 2 by 6:
Equation 1: 727 = p - w ---> Equation 1'
Equation 2: 887 = p + w ---> Equation 2'
Now, let's solve the system of equations:
Adding Equation 1' and Equation 2', we get:
727 + 887 = (p - w) + (p + w)
1614 = 2p
Dividing both sides by 2:
1614/2 = p
807 = p ---> Equation 3
Substituting Equation 3 into Equation 2', we can solve for 'w':
887 = 807 + w
w = 887 - 807
w = 80
Therefore, the rate of the plane in still air (p) is 807 km/h, and the rate of the wind (w) is 80 km/h.