Answer
Wind speed $60$ km/hr and airplane speed $300$ km/hr
Work Step by Step
Step 1. Assume the speed of the wind and the speed of the airplane in still air are $x$ and $y$ km/hr
Step 2. When traveling against the wind, the resulting speed would be $y-x$, and we have $2.5(y-x)=600$
or $-x+y=240$
Step 3. When traveling with the wind, the resulting speed would be $x+y$, and we have $\frac{50}{60}(x+y)=300$ or $x+y=360$
Step 4. Add up the two equations obtained in steps 2 and 3, we get $2y=600$ or $y=300$, thus $x=60$
Step 5. Conclusion: the speed of the wind and the speed of the airplane in still air are $60$ and $300$ km/hr
