In a flight of 1200 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the flight time increased by one hour. What was the original duration of the flight?

1. A

   2 hours

2. B

   4 hours

3. C

   1 hour

4. D

   3 hours

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

• The problem describes a relationship between speed, distance, and time, where the original speed is 1200/t and the new speed is 1200/(t+1).
• The difference between the original and new speed is given as 200 km/hr, which allows the formation of the equation: (1200/t) - (1200/(t+1)) = 200.
• Solving this equation simplifies to a quadratic equation: t² + t - 6 = 0.
• Factoring the quadratic equation gives two possible solutions for t: -3 and 2.
• Since time cannot be negative, the only logical and physically possible answer is that the original duration (t) was 2 hours.

Why Other Options Were Wrong

• Option B: If the original time was 4 hours, the original speed would be 1200/4 = 300 km/hr. The new time would be 5 hours, and the new speed 1200/5 = 240 km/hr. The speed difference is only 60 km/hr, not the 200 km/hr stated in the problem.
• Option C: If the original time was 1 hour, the original speed would be 1200 km/hr. The new time would be 2 hours, and the new speed 1200/2 = 600 km/hr. The speed difference is 600 km/hr, which is incorrect.
• Option D: If the original time was 3 hours, the original speed would be 1200/3 = 400 km/hr. The new time would be 4 hours, and the new speed 1200/4 = 300 km/hr. The speed difference is 100 km/hr, not 200 km/hr. Note that 3 hours is the new duration of the flight, not the original one.

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Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a word problem involving speed, distance, and time using quadratic equations as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of logical-mathematical problem tests critical thinking and analytical skills, which are essential for nurses in various situations, such as calculating drug dosages, IV infusion rates, or interpreting patient data trends.
• Accuracy in calculation is a critical patient safety skill. A small mathematical error can have significant consequences in a clinical setting.
• What if the flight time had decreased by 30 minutes (0.5 hours) and the speed increased by 100 km/hr? The setup would change to: New time = (t - 0.5), New speed = (s + 100). The equation would be (1200/(t-0.5)) - (1200/t) = 100, leading to a different solution and demonstrating the importance of carefully reading the problem parameters.

How to Approach the Question

• First, carefully read the problem to identify all the knowns and unknowns. Knowns: Distance = 1200 km, increase in time = 1 hr, decrease in speed = 200 km/hr. Unknown: Original time (let's call it 't').
• Use the fundamental formula: Speed = Distance / Time. Write expressions for the original speed and the new speed in terms of the unknown 't'.
• Set up an equation based on the relationship given in the problem. Here, the key is that the difference between the original speed and the new speed is 200.
• Solve the resulting algebraic equation. This will often lead to a quadratic equation.
• Evaluate the solutions obtained. In real-world problems involving time, distance, or other physical quantities, negative solutions are usually not valid and should be discarded.
• Finally, perform a quick check by plugging your answer back into the original conditions to ensure it makes sense and satisfies all parts of the problem.

Concept Tested & Keywords

• Concept Tested: Solving a word problem involving speed, distance, and time using quadratic equations.
• Stem keywords: flight, 1200 km, slowed down, bad weather, average speed, reduced by 200 km/hr, time increased by one hour, original duration
• Lead-in keywords: What was

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QcMpr4HA5-X52uaDNI-207

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