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?

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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?

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

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