Final answer:
The question involves solving an equation to find the speed of a jet when factoring in head and tail winds. It requires setting up an equation with the jet's ground speed against the wind (s - 32 mph) for a distance of 1280.2 miles and with the wind (s + 32 mph) for a distance of 1753.8 miles and solving for s, the jet's speed in still air.
Step-by-step explanation:
The student is asking a question about determining the speed of a jet when it is influenced by a head wind and a tail wind while flying different distances in the same amount of time. Given the distances and wind speed, we need to find the plane's airspeed or speed in still air.
Let s be the speed of the jet in still air, and we already know the speed of the wind is 32 mph.
When the jet is flying against the head wind, its ground speed would be s - 32 mph and it covers 1280.2 miles. When the jet is flying with the tail wind, its ground speed would be s + 32 mph and it covers 1753.8 miles.
To find the time t, we can say:
t = 1280.2 / (s - 32) = 1753.8 / (s + 32).
By solving this equation for s, we can find the speed of the jet in still air.