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?
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?
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Let the planes speed in still air = s
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Speed with the wind: (s+30)
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Speed against the wind: (s-30)
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Distance out and back is the same; 720 mi
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Write a time equation: Time = dist/speed
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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:
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720(s+30) + 720(s-30) = 10(s-30)(s+30)
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720s + 21600 + 720s - 21600 = 10(s^2 - 900)
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1440s = 10s^2 - 9000
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0 = 10s^2 -1440s - 9000 a quadratic equation
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s^2 - 144s - 900 = 0 Simplified, divided equation by 10
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Factors to: (s + 6) (s - 150) = 0
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Obvious solution: s = +150 mph
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Check:
720/120 + 720/180 =
6 + 4 = 10 hrs
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could you follow this OK?
