In a flight of 1500 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/h and the time of flight was increased by 2 hours. What was the original duration of the flight?

1. A

   2 h

2. B

   5 h

3. C

   4 h

4. D

   3 h

Appeared in: DSSSB - 29 August 2019 (Shift-2)

Explanation

• The problem requires setting up equations based on the formula Speed = Distance / Time.
• Let the original time be 't'. The original speed is 1500/t. The new time is (t+2) and the new speed is 1500/(t+2).
• The difference in speed is given as 200 km/h, leading to the equation: (1500/t) - (1500/(t+2)) = 200.
• Solving this equation yields a quadratic equation: t^2 + 2t - 15 = 0.
• Factoring gives (t+5)(t-3) = 0. Since time cannot be negative, the only valid solution is t = 3 hours.
• Verification: Original speed = 1500/3 = 500 km/h. New speed = 1500/(3+2) = 300 km/h. The difference is 500 - 300 = 200 km/h, which matches the problem statement.

Why Other Options Were Wrong

• Option A: If the original time was 2 hours, the original speed would be 1500/2 = 750 km/h. The new time would be 4 hours, and the new speed 1500/4 = 375 km/h. The speed difference is 375 km/h, which is not the 200 km/h stated in the problem.
• Option B: If the original time was 5 hours, the original speed would be 1500/5 = 300 km/h. The new time would be 7 hours, and the new speed 1500/7 ≈ 214.3 km/h. The speed difference is approximately 85.7 km/h, not 200 km/h.
• Option C: If the original time was 4 hours, the original speed would be 1500/4 = 375 km/h. The new time would be 6 hours, and the new speed 1500/6 = 250 km/h. The speed difference is 125 km/h, not 200 km/h.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving word problems involving the relationship between distance, speed, and time as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude, a common component of nursing entrance examinations designed to assess general intelligence and problem-solving skills.
• It evaluates the ability to translate a real-world scenario into a mathematical model and solve it, a skill that underpins logical reasoning and critical thinking in any professional field, including nursing.
• What if the speed was increased by 100 km/h and the time decreased by 1 hour? The setup would change to (1500/(t-1)) - (1500/t) = 100. This requires a different calculation but follows the same logical process of setting up and solving an equation.

How to Approach the Question

• First, identify the knowns (Distance = 1500 km) and the relationships between the variables (speed reduced by 200 km/h, time increased by 2 hours).
• Define a variable for the unknown you need to find. Let 't' be the original duration of the flight.
• Express the original speed and the new speed in terms of 't' using the formula Speed = Distance / Time.
• Set up an equation based on the given change in speed: Original Speed - New Speed = 200.
• Solve the resulting algebraic equation (which becomes a quadratic equation) for 't'.
• Discard any non-physical solutions, such as negative time.

Concept Tested & Keywords

• Concept Tested: Solving word problems involving the relationship between distance, speed, and time.
• Stem keywords: flight, 1500 km, slowed down, bad weather, average speed, reduced by 200 km/h, time, increased by 2 hours
• Lead-in keywords: What was

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