SOLUTION: 1. A plane flies 720 miles against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane's speed in still air
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Question 53603: 1. A plane flies 720 miles against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane's speed in still air?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. A plane flies 720 miles against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10h, what is the plane's speed in still air?
:
Let the planes speed in still air = s
:
Speed with the wind: (s+30)
:
Speed against the wind: (s-30)
:
Distance out and back is the same; 720 mi
:
Write a time equation: Time = dist/speed
:
Time out + time back = 10 hrs
+ = 10
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To get rid of the denominators, mult eq by (s-30)(s+30), resulting in:
:
720(s+30) + 720(s-30) = 10(s-30)(s+30)
:
720s + 21600 + 720s - 21600 = 10(s^2 - 900)
:
1440s = 10s^2 - 9000
:
0 = 10s^2 -1440s - 9000 a quadratic equation
:
s^2 - 144s - 900 = 0 Simplified, divided equation by 10
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Factors to: (s + 6) (s - 150) = 0
:
Obvious solution: s = +150 mph
:
:
Check:
720/120 + 720/180 =
6 + 4 = 10 hrs
:
could you follow this OK?
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