An aeroplane has to cover a distance of 1 200 km. Due to bad weather it reduces its speed by 300 km/h and therefore reaches the destination 2 hours late. What was the scheduled duration of the flight in hours under normal speed conditions?

Introduction / Context:

This question involves forming an equation using the time, speed and distance relationship when the speed of an aeroplane changes. The plane was supposed to fly at a higher normal speed but due to bad weather it reduces its speed by a fixed amount and arrives 2 hours later than scheduled. We are asked to find the originally planned duration of the flight, not the speed directly. This is a classic algebraic application in time and distance.

Given Data / Assumptions:

• Planned distance = 1 200 km.
• Normal speed = v km/h (unknown).
• Reduced speed = v - 300 km/h.
• Distance remains 1 200 km in both scenarios.
• Actual flight time = scheduled time + 2 hours.

Concept / Approach:

Time taken for a given distance is distance / speed. Let the scheduled time be T hours, so T = 1 200 / v. With reduced speed the time becomes 1 200 / (v - 300). We are told that the new time is 2 hours more than the original time. Therefore, 1 200 / (v - 300) = 1 200 / v + 2. This equation can be solved for v and then we can compute T. Since the question asks for the duration, our final answer is T in hours.

Step-by-Step Solution:

Verification / Alternative check:

With v = 600 km/h, the normal time is 1 200 / 600 = 2 hours. The reduced speed is 600 - 300 = 300 km/h. At this reduced speed, time = 1 200 / 300 = 4 hours. The difference between the delayed time and the scheduled time is 4 - 2 = 2 hours, which matches the given condition. Therefore the scheduled duration of 2 hours is correct.

Why Other Options Are Wrong:

If the scheduled time were 1 hour, the normal speed would need to be 1 200 km/h, giving a reduced speed of 900 km/h which would not result in only 2 hours extra. A scheduled time of 1.5 hours or 2.5 hours leads to speeds and delayed times that do not give a difference of exactly 2 hours. Only a scheduled duration of 2 hours corresponds to a realistic speed of 600 km/h and a reduced speed of 300 km/h that fits all the conditions.

Common Pitfalls:

Some learners directly try to guess the speed or time without forming an equation, which can lead to confusion. Others forget to subtract 300 from the normal speed and instead divide by 300, which is incorrect. It is also easy to make algebraic mistakes while solving 1 200 / (v - 300) = 1 200 / v + 2. Writing each step clearly and checking the resulting speed and times helps avoid errors.

Final Answer:

The scheduled duration of the flight under normal conditions was 2 hours.