- plane: 1150 kph
- wind: 250 kph
The given relationships allow us to write a system of equations in the speeds of the wind and plane.
Let w and p represent the speeds of the wind and the plane, respectively. We know speed is the ratio of distance to time, so ...
p -w = 6300 km/(7 h) = 900 km/h
p +w = 8400 km/(6 h) = 1400 km/h
Adding these two equations gives ...
2p = 2300 km/h
p = 1150 km/h . . . . . . divide by 2
Subtracting the first equation from the second gives ...
2w = 500 km/h
w = 250 km/h
The speed of the plane in still air is 1150 km per hour; the speed of the wind is 250 km per hour.