Answer:
The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.
Step-by-step explanation:
From Mechanical Physics, we know that absolute velocity of the airplane ([tex]v_{A}[/tex]) is equal to sum of the absolute velocity of the jet steam [tex](v_{J})[/tex] and the relative velocity of the airplane with respect to jet stream (velocity of the airplane in still air) ([tex]v_{A/J}[/tex]). Al velocities are measured in miles per hour. Let suppose that both jet stream and airplanes travels at constant velocity. Now, we construct the following system of linear equations:
Flight with the jet stream
[tex]v_{J}+v_{A/J} = \frac{2700\,mi}{4.5\,h}[/tex]
[tex]v_{J}+v_{A/J} = 600\,\frac{mi}{h}[/tex] (1)
Flight against the jet stream
[tex]v_{J} -v_{A/J} = -\frac{2700\,mi}{6\,h}[/tex]
[tex]v_{J}-v_{A/J} = -450\,\frac{mi}{h}[/tex] (2)
The solution of this system of linear equations is:
[tex]v_{J} = 75\,\frac{mi}{h}[/tex], [tex]v_{A/J} = 525\,\frac{mi}{h}[/tex]
The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.
