Let x be the speed of the plane at not wind
Let y be the speed of the wind
Flying with the wind the effective speed is:
[tex]x+y[/tex]Flying against the wind the effective speed is:
[tex]x-y[/tex]Speed with the wind: use the distance and time given to calculate the spped:
[tex]\begin{gathered} \frac{240mi}{2h}=120mi/h \\ \\ x+y=120mi/h \end{gathered}[/tex]Speed agains the wind: use the distance and time given to calculate the spped:
[tex]\begin{gathered} \frac{240mi}{3h}=80mi/h \\ \\ x-y=80mi/h \end{gathered}[/tex]System of equations:
[tex]\begin{gathered} x+y=120 \\ x-y=80 \end{gathered}[/tex]Add both equations:
Use 2x=200 to solve x:
[tex]\begin{gathered} 2x=200 \\ \\ x=\frac{200}{2} \\ \\ x=100 \end{gathered}[/tex]Use x=100 to solve y:
[tex]\begin{gathered} x+y=120 \\ 100+y=120 \\ y=120-20 \\ \\ y=20 \end{gathered}[/tex]Then, the rate (speed) of the wind (y) is 20 mi/h
