Final answer:
The rate of the jet in still air is 580 miles per hour, and the rate of the jetstream is 400 miles per hour, determined by using the distance-rate-time relationship and comparing two different scenarios of the jet's flight.
Step-by-step explanation:
The question involves a calculation to determine the rate of a jet in still air and the rate of the jetstream, given two different scenarios. In the first scenario, the jet travels 2320 miles in 4 hours, and in the second scenario, flying with the jetstream, it travels 8820 miles in 9 hours. To solve this, we use the fact that distance equals rate multiplied by time (D = RT).
For the first scenario, without the jetstream, the rate of the jet (Rjet) is 2320 miles / 4 hours = 580 miles per hour. In the second scenario, the rate of the jet with the jetstream (Rtotal) is 8820 miles / 9 hours = 980 miles per hour. The difference between Rtotal and Rjet gives us the rate of the jetstream (Rjs).
Therefore, the rate of the jetstream is Rjs = Rtotal - Rjet = 980 mph - 580 mph = 400 mph. Thus, the rate of the jet in still air is 580 miles per hour and the rate of the jetstream is 400 miles per hour.