What is the rate of the plane in still air and what is the rate of the wind?

Question

An airplane travels 3605km against the wind in 5 hours and 4605km  with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Let P be the Plane's rate (speed) in still air.

Let W by the rate of the Wind.

Then the total rate against the wind will be P - W.

And the total rate WITH the wind will be P+W.

We use our rate formula (Distance = Rate * Time) twice:

3605 = (P-W)*5

4605 = (P+W)*5

Adding the 2 equations together gives us

8210 = 10*P

or

P = 821 km/hr

and

5*W = 5*P - 3605

W = P - 721 = 821 - 721 = 100 km/hr