What is the airplane's average rate in calm air?

Question

The rate of the jet stream is 300mph. Traveling with the jet stream, an airplane can fly 3600 miles in the same amount of time as it takes to fly 1200 miles against the jet stream. What is the aiplane's average rate in calm air?

Answer 1

Let x = speed of plane in calm air

 

x + 300 = rate with the jet stream

x - 300 = rate against the jet stream

 

Distance = (Rate)(Time), so Time = (Distance)/(Rate)

 

Time with jet stream = Time against jet stream

 

3600/(x+300) = 1200/(x-300)

 

Cross multiply to get 3600(x-300) = 1200(x+300)

 

                 Divide by 1200:  3(x-300) = x+300

 

                                        3x - 900 = x + 300

 

                                                2x = 1200

 

                                                 x = 600 mph