Respuesta :
ANSWER:
Plane: 795km/h
Wind: 60km/h
STEP-BY-STEP EXPLANATION:
We have that the speed is given as follows:
[tex]\begin{gathered} v=\frac{d}{t} \\ \\ d=vt \end{gathered}[/tex]We know that time is constant, therefore we can establish the following:
[tex]\begin{gathered} 3675=5\cdot(v_{plane}-v_{wind})\rightarrow3675=5v_{plane}-5v_{wind} \\ \\ 4275=5\cdot(v_{plane}+v_{wind})\rightarrow4275=5v_{plane}+5v_{wind} \end{gathered}[/tex]We can solve the system by adding both equations, like this:
[tex]\begin{gathered} 3675+4275=5v_{plane}-5v_{wind}+5v_{plane}+5v_{wind} \\ \\ 7950=10v_{plane} \\ \\ v_{plane}=\frac{7950}{10}=795\text{ km/h} \\ \\ \text{ To calculate the air rate it would be like this:} \\ \\ 4275=5v_{plane}+5v_{wind} \\ \\ 4275=5\cdot795+5v_{wind} \\ \\ 5v_{wind}=4275-3975 \\ \\ v_{wind}=\frac{300}{5}=60\text{ km/h} \\ \end{gathered}[/tex]This means that the rate of the plane in still air is 795 km/h and the rate of the wind is 60 km/h
