In a flight of 900 km, Air-India Express was slowed down due to bad weather.…

Step-by-Step Solution

To find the actual duration of the flight, we can set up an algebraic equation based on the relationship between distance, speed, and time.

1. Define the variables:

   • Let the original duration of the flight be x hours.

   • The increased duration due to bad weather is x + 0.5 hours (since 30 minutes = 0.5 hours).

   • Total distance = 900 km.

2. Set up the speed equation:

   • The difference in speed is 300 km/hr.

   • 900/x - 900/(x + 0.5) = 300

3. Solve for x:

   • Divide the entire equation by 300:

   • 3/x - 3/(x + 0.5) = 1

   • 3 * (x + 0.5) - 3x = x * (x + 0.5)

   • 3x + 1.5 - 3x = x^2 + 0.5x

   • x^2 + 0.5x - 1.5 = 0

   • Multiply by 2 to clear decimals: 2x^2 + x - 3 = 0

   • Factor the quadratic equation: (2x + 3)(x - 1) = 0

   • Since time cannot be negative, x = 1 hour.

4. Calculate the actual duration:

   • The actual duration of the flight is the increased time: x + 0.5 = 1 + 0.5 = 1.5 hours.