What are the wind, speed, and the speed of the plane in still air?

Question

A cross-country flight traveling with the wind covers 3000 miles in 5 hours. The same plane then changes direction and travels to Texas, against the wind, covering 1500 miles in 3 hours. 

Answer 1

distance = rate * time

3000 = (x+y)* 5 ---> x+y = 600

1500 = (x-y)*3 ---> x-y = 500

2x = 1100

x = 550

this forces y=50

the speed of the plane is 550

the speed of the wind is 50