Answer:
Velocity of airplane is 500 km/h
Velocity of wind is 40 km/h
Explanation:
[tex]V_a[/tex]= Velocity of airplane in still air
[tex]V_w[/tex]= Velocity of wind
Time taken by plane to travel 1150 km against the wind is 2.5 hours
[tex]V_a-V_w=\frac {1150}{2.5}\\\Rightarrow V_a-V_w=460\quad (1)[/tex]
Time taken by plane to travel 450 km against the wind is 50 minutes = 50/60 hours
[tex]V_a+V_w=\frac {450}{50}\times 60\\\Rightarrow V_a-V_w=540\quad (2)[/tex]
Subtracting the two equations we get
[tex]V_a-V_w-V_a-V_w=460-540\\\Rightarrow -2V_w=-80\\\Rightarrow V_w=40\ km/h[/tex]
Applying the value of velocity of wind to the first equation
[tex]V_a-40=460\\\Rightarrow V_a =500\ km/h[/tex]
∴ Velocity of airplane in still air is 500 km/h and Velocity of wind is 40 km/h
