Flying against the wind, an airplane travels
6840km
in
9
hours. Flying with the wind, the same plane travels
3000km
in
3
hours. What is the rate of the plane in still air and what is the rate of the wind?

Question

Flying against the wind, an airplane travels 
6840km
 in 
9
 hours. Flying with the wind, the same plane travels 
3000km
 in 
3
 hours. What is the rate of the plane in still air and what is the rate of the wind?

anonymous · Answer

Do you understand what rate means? 
HINT: The plane's airspeed is the average.

anonymous · Answer

The wind speed is the difference

whpalmer4 · Answer

If we let $w_p$ be the speed of the airplane in still air, and $w_s$ be the speed of the wind, then we can figure this out with the rate equation: $$d = s t$$

Flying against the wind, we have
$$6840 \text{ km} = (w_p-w_s)(9\text{ hours})$$Flying with the wind, we have
$$3000\text{ km} = (w_p+w_s)(3\text{ hours})$$For clarity, we can drop the units (remembering that we are doing everything in km/hr):
$$6840 = 9(w_p-w_s)$$$$3000=3(w_p+w_s)$$expanding to
$$6840=9w_p-9w_s$$$$3000=3w_p+3w_s$$which is a system of two equations in two unknowns, easily solved for the speed of the plane and the wind.