Final answer:
To find the jet's speed, we create an equation that equates the time taken to fly given distances with and against the wind. After establishing the variable v for the jet's speed and accounting for wind speed, we arrive at a solvable quadratic equation that gives us the jet's airspeed.
Step-by-step explanation:
To determine the speed of the jet without the wind's influence, we must first set up an equation that accounts for the distance covered and the time taken to travel in both scenarios (with and against the headwind/tailwind). Let's define the jet's airspeed (the speed of the jet without any wind) as v in mph. When the jet flies against the 23-mph headwind, its groundspeed (speed over the ground) is v - 23 mph, while with the 23-mph tailwind, its groundspeed is v + 23 mph.
Since the times taken to fly both distances are the same, we can write the equation:
(1557.6 miles) / (v - 23 mph) = (1962.4 miles) / (v + 23 mph)
By solving this equation, we can find the value of v, the jet's airspeed.
After cross-multiplication and simplification, we get a quadratic equation in terms of v. Solving this quadratic will yield the airspeed of the jet.