Final answer:
The speed of the jet in still air is calculated using the relationship between distance, rate, and time for the two different scenarios of flying with a tailwind and against a headwind. By setting up equations for each scenario and solving for the jet's speed in still air, we determine that the jet's speed is 170 mph.
Step-by-step explanation:
To find the speed of the jet in still air, you need to use the concept that distance equals rate times time (D = RT). Given that the jet can fly 1343.2 miles against a 24-mph headwind and 1784.8 miles with a 24-mph tailwind in the same amount of time, we can set up two equations to represent these situations.
- Against the wind: D1 = (r - 24)t
- With the wind: D2 = (r + 24)t
Where:
- D1 = 1343.2 miles
- D2 = 1784.8 miles
- r is the speed of the jet in still air
- t is the time in hours
Since the time is the same for both trips, we can equate the two equations:
1343.2 / (r - 24) = 1784.8 / (r + 24)
Solving this equation gives you the jet's speed:
- 1343.2(r + 24) = 1784.8(r - 24)
- 1343.2r + 32237.6 = 1784.8r - 42835.2
- 441.6r = 75072.8
- r = 170 mph (jet's speed in still air)
The jet's speed in still air is therefore 170 mph.