The speed of the airplane is the ratio of the distance to the time
The initial average speed of the airplane is approximately 110.8 mph
Reason:
Given parameters are;
The distance between Portland Oregon and Seattle Washington = 145 miles
The decrease in travel time when the speed is increase by 20 mph = minutes
The initial speed of the airplane, v = Required;
Solution;
[tex]t = \dfrac{145}{v}[/tex]
[tex]t - \dfrac{12}{60} = \dfrac{145}{v + 20}[/tex]
Therefore;
[tex]\dfrac{145}{v} - \dfrac{12}{60} = \dfrac{145}{v + 20}[/tex]
Which gives;
[tex]\dfrac{145}{v + 20} - \dfrac{145}{v} + \dfrac{12}{60} = 0[/tex]
Therefore
0.2·v² + 4·v - 2,900 = 0
v ≈ ±110.8 mph
The initial average speed of the airplane, v≈ ± 110.8 mph
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