In a 600 km flight, bad weather reduces the average speed by 200 km/h and increases the time by 30 minutes. What is the original duration of the flight?

Let the planned (normal) duration be t hours for a 600 km flight. Then planned speed = 600 / t km/h. Due to bad weather, average speed is reduced by 200 km/h and the flight takes 30 minutes (0.5 h) longer.

Concept / Approach
We relate speed and time before and after delay using Speed = Distance / Time for the same distance (600 km), and then solve for t.

Step-by-step calculation
Planned speed = 600 / tReduced speed = 600 / (t + 0.5)Given: (600 / t) − 200 = 600 / (t + 0.5)Solve for t:600 / t − 600 / (t + 0.5) = 200600[(t + 0.5) − t] / [t(t + 0.5)] = 200600(0.5) / [t(t + 0.5)] = 200300 / [t(t + 0.5)] = 200t(t + 0.5) = 300 / 200 = 1.5t² + 0.5t − 1.5 = 0The positive root is t = 1.

Verification
Planned speed = 600 / 1 = 600 km/hReduced speed = 600 / 1.5 = 400 km/hDrop in speed = 600 − 400 = 200 km/h (matches)Time increase = 1.5 − 1 = 0.5 h = 30 min (matches)

Common pitfalls
Confusing the “duration of the flight” with the delayed duration. The question asks for the original duration, not the delayed 1.5 hours.

Final Answer
1 hour