Answer: the rate of the plane in still air is 550 mph and the rate of the wind is 50 mph
Step-by-step explanation:
Let x represent the rate of the plane in still air.
Let y represent the rate of the wind.
When a plane flies into the wind, it can travel 3000 miles in 6 hours. The total speed with which the plane flew is x - y
Distance = speed × time
Therefore,
3000 = 6(x - y)
Dividing through by 6, it becomes
500 = x - y - - - - - - - - - - - - - -1
When it flies with the wind, it can travel the same distance in 5 hours.
The total speed with which the plane flew is x + y
Distance = speed × time
Therefore,
3000 = 5(x + y)
Dividing through by 5, it becomes
600 = x + y - - - - - - - - - - - - - -2
Adding equation 1 to equation 2, it becomes
1100 = 2x
x = 1100/2 = 550
Substituting x = 550 into equation 1, it becomes
500 = 550 - y
y = 550 - 500
y = 50
