Final answer:
The plane's rate in still air is 1010 km/h and the wind's rate is 250 km/h, calculated using two equations derived from distance, rate, and time for flying against and with the wind.
Step-by-step explanation:
To determine the rate of the plane in still air and the rate of the wind, we can set up a system of equations based on the information given. Let p be the speed of the plane in still air, and w be the speed of the wind.
Flying Against the Wind
When flying against the wind, the speed of the plane relative to the ground is p - w. Considering the formula distance = rate × time, the equation for flying against the wind for 9 hours is:
6840 km = (p - w) × 9 hours (1)
Flying With the Wind
When flying with the wind, the speed of the plane relative to the ground is p + w. The equation for flying with the wind for 8 hours is:
10080 km = (p + w) × 8 hours (2)
Solving the System of Equations
Now, we can solve the system of equations (1) and (2) simultaneously:
From equation (1), p - w = 6840 km/9 hours
= 760 km/h
From equation (2), p + w = 10080 km/8 hours
= 1260 km/h
Adding these two equations together, we get:
2p = 760 km/h + 1260 km/h
2p = 2020 km/h
p = 1010 km/h (Speed of plane in still air)
Substituting the value of p back into equation (1) or (2):
w = 1260 km/h - p
w = 1260 km/h - 1010 km/h
w = 250 km/h (Speed of wind)
The rate of the plane in still air is 1010 km/h, and the rate of the wind is 250 km/h.