## anonymous one year ago 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?

1. anonymous

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

2. anonymous

The wind speed is the difference

3. whpalmer4

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.