In a flight of 800 km, an aircraft was slowed down due to bad weather. Its…

Concept: If a fixed distance is covered in two different times, the two average speeds are Distance divided by Time in each case. When the difference between these two speeds is given, it sets up an equation in the unknown time, which often reduces to a quadratic whose roots must be checked for physical validity (a duration cannot be negative).

Application: Let the original (scheduled) duration of the flight be x hours. Because of the delay, the new duration becomes x + 2 hours. Original speed = 800/x km/hr. New (reduced) speed = 800/(x+2) km/hr. The question states the original speed exceeds the new speed by 200 km/hr.

1. 800/x - 800/(x+2) = 200

2. Divide both sides by 200: 4/x - 4/(x+2) = 1

3. Take the LCM on the left: [4(x+2) - 4x] / [x(x+2)] = 1, which gives 8 = x(x+2)

4. x2 + 2x - 8 = 0

5. Factorise: (x + 4)(x - 2) = 0

6. x = -4 or x = 2; reject x = -4 since a duration cannot be negative, so x = 2

Cross-check: With x = 2 hours, the original speed = 800/2 = 400 km/hr and the new speed = 800/4 = 200 km/hr. The difference is 400 - 200 = 200 km/hr, exactly matching the condition given in the question - confirming the original duration is 2 hours.