Final answer:
To determine the speed of the jet in still air and the speed of the jetstream, we solve two linear equations resulting from the jet's travel times against and with the jetstream, yielding a jet speed of 780 miles/hour and a jetstream speed of 200 miles/hour.
Step-by-step explanation:
The question involves solving two linear equations to determine the speed of the jet in still air and the speed of the jetstream. Flying against the jetstream, the jet travels 2320 miles in 4 hours, which gives us the first equation:
Speed of jet in still air (s) - Speed of jetstream (j) = 580 miles/hour (1)
Flying with the jetstream, the jet travels 8820 miles in 9 hours, leading to the second equation:
Speed of jet in still air (s) + Speed of jetstream (j) = 980 miles/hour (2)
To solve this system, we can add the two equations together to eliminate the jetstream variable:
2s = 580 miles/hour + 980 miles/hour
Thus, we find that the speed of the jet in still air is s = 780 miles/hour. Subtracting the first equation from the second helps us find the speed of the jetstream:
2j = 980 miles/hour - 580 miles/hour
The speed of the jetstream is j = 200 miles/hour.