Final answer:
The rate of the jet in still air is 890 miles per hour and the rate of the jet stream is 180 miles per hour.
Step-by-step explanation:
To find the rate of the jet in still air and the rate of the jet stream, we can set up two equations using the given information.
Let's use x to represent the rate of the jet in still air and y to represent the rate of the jet stream.
From the first scenario, flying against the jet stream, we can use the equation: x - y = 4970/7.
Solving this equation, we get x - y = 710.
From the second scenario, flying with the jet stream, we can use the equation: x + y = 8560/8.
Solving this equation, we get x + y = 1070.
Now, we can solve these two equations simultaneously to find the values of x and y.
Adding the two equations, we get 2x = 1780, which gives us x = 890.
Substituting this value into one of the equations, we get 890 + y = 1070, which gives us y = 180.
Therefore, the rate of the jet in still air is 890 miles per hour and the rate of the jet stream is 180 miles per hour.