Richard needs to fly from San Diego to Halifax, Nova Scotia and back in order to give an important talk about mathematics. On the way to Halifax, he will get a speed boost from the wind which blows at 50 miles per hour (mph). On the way back, the plane must, unfortunately, fight this wind speed. If the talk lasts 5 hours, and if the distance between the two cities is \(2000\) miles, how fast must the plane fly in mph if the entire trip is to take \(12\) hours?
+128474 Remember that Distance / Rate = Tme
Let the plane speed in still air = P
Time to fly to tthe meeting with the wind = 2000 / (P + 50)
Time to return = 2000 / ( P - 50)
So
simplify
2000 / (P + 50) + 2000 / (P -50) = 7
2000 (P- 50) + (2000)(P+50) = 7 (P + 50)(P -50)
4000P = 7 (P^2 - 2500)
7P^2 - 4000P - 17500 = 0
Using the Quadratic Formula
4000 ± sqrt [ 4000^2 - 4 * 7 * (-17500) ] 4000 + 4060.79
_________________________________ = ________________ = P ≈ 576 mph
2 (7) 14
