Answer: the speed of the wind is 66 mph and the speed of the plane in still air is 462 mph
Step-by-step explanation:
Let x represent the speed of the plane in still air.
Let y represent the speed of the wind.
The distance between city A and city B is 792 miles.
On one particular trip, they fly into the wind, and the flight takes 2 hours. This means that the total speed at which they flew is (x - y) mph.
Distance = speed × time
Distance travelled against the wind is expressed as
792 = 2(x - y)
Dividing through by 2, it becomes
396 = x - y- - - - - - - -1
The return trip with the wind behind them, it took 1 and one half hours. This means that the total speed at which they flew is (x + y) mph. Distance travelled with the wind is expressed as
792 = 1.5(x + y)
Dividing through by 1.5, it becomes
528 = x + y- - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
924 = 2x
x = 924/2
x = 462 mph
Substituting x = 462 into equation 2, it becomes
528 = 462 + y
y = 528 - 462
y = 66 mph
