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help algebra

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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?

Apr 27, 2022

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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

4000 ±  sqrt  [ 4000^2  - 4 * 7 * (-17500)  ]                     4000 + 4060.79

_________________________________        =         ________________   =  P   ≈   576 mph

2 (7)                                                                      14

Apr 27, 2022
edited by CPhill  Apr 27, 2022