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In a flight of 600 kms, an aircraft was slowed down due to bad weather and the average speed was reduced by 200 km/hour, and the time of flight increased by 30 minutes. What is the total duration of flight?
  1. 1 hour
  2. 2 hours
  3. 3 hours
  4. 4 hours
Explanation

  • Equation Setup:

    • In bad weather:600 = (v - 200)(t + 0.5)
    • In good weather:
    • Solving for vv

  • Substituting vv in the first equation:


    600 = left(frac{600}{t} - 200right)(t + 0.5)

  • Expanding and simplifying the equation:


    600t = 600t + 300 - 200^2 - 100t
    -200t^2 - 100t + 300 = 0
    2t^2 + t - 3 = 0

  • Solving the quadratic equation:


    2t^2 + 3t - 2t - 3 = 0    2t(t - 1) + 3(t - 1) = 0(2t + 3)(t - 1) = 0

  • Finding values for tt:

    2t + 3 = 0 quad text{or} quad t - 1 = 0
    t = 1 quad text{(valid answer)}

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