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 hour

2 hours

3 hours

4 hours

Equation Setup:

Substituting $v$ 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 $t$ :

$2t + 3 = 0 quad text{or} quad t - 1 = 0$ $2 t = - 3 \Rightarrow t = - \frac{3}{2} (negative, not possible)$ $t = 1 quad text{(valid answer)}$