In a flight of 1800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 300 km/h and the time of flight was increased by 3 hours. What was the original duration of the flight?

1. A

   5 hours

2. B

   4 hours

3. C

   3 hours

4. D

   6 hours

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

• The problem can be modeled with two equations: 1800 = s × t (original) and 1800 = (s - 300) × (t + 3) (new).
• By substituting s = 1800/t into the second equation, we derive a quadratic equation for time: t² + 3t - 18 = 0.
• Factoring the equation gives (t - 3)(t + 6) = 0. Since time cannot be negative, the only valid solution is t = 3 hours.

Why Other Options Were Wrong

• Option A: If the original time was 5 hours, the original speed would be 360 km/h. The new speed would be 60 km/h, and the new time would be 30 hours. This is a time increase of 25 hours, not 3.
• Option B: If the original time was 4 hours, the original speed would be 450 km/h. The new speed would be 150 km/h, and the new time would be 12 hours. This is a time increase of 8 hours, not 3.
• Option D: 6 hours is the new, increased time of flight, not the original duration. The question asks for the original duration.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving quadratic equations derived from word problems involving speed, distance, and time as background academic context rather than a clinical decision trigger.
• While this is a general aptitude question, the underlying mathematical skill is crucial in nursing for calculations involving rates, such as IV drip rates, medication dosages over time, and fluid balance monitoring.
• For example, calculating the time required to infuse a certain volume of fluid at a given rate (Time = Volume / Rate) uses the exact same logical structure as this problem.
• What if? If the flight was 2400 km and the speed was reduced by 200 km/h, increasing the time by 2 hours, the same method would be applied. The equation would become t² + 2t - 24 = 0, leading to an original time of 4 hours.

How to Approach the Question

• First, identify all the numerical values and the relationships described in the word problem (e.g., distance, speed reduction, time increase).
• Define variables for the unknown quantities you need to find, such as 's' for original speed and 't' for original time.
• Translate the relationships from the problem into mathematical equations. You will likely have a system of two equations.
• Solve the system of equations. This often involves substituting one equation into the other to get a single equation with one variable.
• Solve the resulting equation (in this case, a quadratic equation) for the variable. Discard any non-physical solutions (like negative time).
• Always double-check your answer by plugging it back into the original problem statement to ensure it makes sense.

Concept Tested & Keywords

• Concept Tested: Solving quadratic equations derived from word problems involving speed, distance, and time.
• Stem keywords: flight, 1800 km, slowed down, average speed reduced, 300 km/h, time increased, 3 hours
• Lead-in keywords: original duration
• Negative lead-in flag: false

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QJPKsneODl3FhlOIr22gNb

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