Answer: rate of the plane is 197.5 mph
rate of wind is 4.5 mph
Step-by-step explanation:
Let x represent the rate of the plane in calm air.
Let y represent the rate of the wind.
Flying with the wind, a small plane flew 404 mi in 2 h. This means that the total speed with which the plane flew is (x + y) mph.
Distance = speed × time
Distance travelled by the plane while flying with the wind is
404 = 2(x + y)
Dividing both sides of the equation by 2, it becomes
202 = x + y- - - - - - - - - - - 1
Flying against the wind, the plane could fly only 386 mi in the same amount of time. This means that the total speed at which the plane flew is (x - y) mph.
Distance = speed × time
Distance travelled by the plane while flying against the wind is
386 = 2(x - y)
Dividing both sides of the equation by 2, it becomes
193 = x - y- - - - - - - - - - - 2
Adding equation 1 to equation 2, it becomes
395 = 2x
x = 395/2
x = 197.5
Substituting x = 197.5 into equation 1, it becomes
202 = 197.5 + y
y = 202 - 197.5
y = 4.5
