Respuesta :
Answer:
The rate of airplane in still air [tex]=710\ km\ hr^{-1}[/tex]
The rate of the wind is [tex]=160\ km \ hr^{-1}[/tex]
Step-by-step explanation:
Let the speed of the airplane be [tex]s_{a}[/tex]
And the speed of the wind be [tex]s_{w}[/tex]
So we know that, [tex]Speed = \frac{distance}{time}[/tex]
According to the question.
When the airplane is flying with the wind it will be supported by the wind.
So the speed, [tex]=s_{w}+s_{a} =\frac{6090}{7}[/tex]
[tex]=s_{w}+s_{a} =870[/tex]
[tex]=s_{w}=870-s_{a}[/tex]... equation (1)
When the airplane is flying with against the wind it will be negated by the wind.
Then the speed , [tex]=s_{a}-s_{w}=\frac{2750}{5}[/tex]... equation (2)
Plugging the values from equation (1)....
[tex]=s_{a}-(870-s_{a})=550[/tex]
[tex]=2s_{a}=550+870[/tex]
[tex]=2s_{a}=\frac{550+870}{2}=710[/tex]
So rate of airplane in still air [tex]=710\ km\ per\ hr[/tex]
Now to find the rate of wind we can plug the values of rate of airplane in equation (1).
Then we have
[tex]=s_{w}+s_{a} =870[/tex]
[tex]=s_{w}=870-710=160[/tex]
So the rate of the wind that is [tex]=s_{w}=160\ km\ per \hr[/tex]
The rate of airplane in still air [tex]=710\ km\ per\ hr[/tex] and rate of the wind is [tex]=s_{w}=160\ km\ per\ \hr[/tex]
