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: JIPMER Nursing Officer - 2020

Explanation

• Let the original time be 't' hours. The original speed is therefore 1800/t km/h.
• The new time is (t + 3) hours, and the new speed is 1800/(t + 3) km/h.
• The difference in speed is given as 300 km/h, which leads to the equation: (1800/t) - (1800/(t + 3)) = 300.
• Simplifying and solving this equation results in a quadratic equation: t² + 3t - 18 = 0.
• Factoring the quadratic equation gives (t - 3)(t + 6) = 0.
• Since time cannot be negative, the only logical and physically possible solution is t = 3 hours.

Why Other Options Were Wrong

• Option A: If the original time was 5 hours, the original speed would be 1800/5 = 360 km/h. The new time would be 8 hours, and the new speed 1800/8 = 225 km/h. The difference is 360 - 225 = 135 km/h, which is not the 300 km/h stated in the problem.
• Option B: If the original time was 4 hours, the original speed would be 1800/4 = 450 km/h. The new time would be 7 hours, and the new speed 1800/7 ≈ 257.14 km/h. The difference is approximately 192.86 km/h, not 300 km/h.
• Option D: If the original time was 6 hours, the original speed would be 1800/6 = 300 km/h. The new time would be 9 hours, and the new speed 1800/9 = 200 km/h. The difference is 300 - 200 = 100 km/h, not 300 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 time, speed, and distance using algebraic equations as background academic context rather than a clinical decision trigger.
• While not a clinical question, the logical reasoning and mathematical accuracy required are essential skills for nurses.
• Nurses frequently perform calculations for drug dosages, IV infusion rates, and fluid balance, where a mistake can have serious consequences for patient safety.
• This type of problem-solving strengthens the analytical skills needed to interpret patient data and manage time-sensitive clinical tasks effectively.

How to Approach the Question

• First, identify the core relationship: Distance = Speed × Time. Note the constant value (Distance = 1800 km).
• Define a single variable for the unknown you need to find. Let the original time be 't'.
• Express all other quantities in terms of 't'. Original Speed = 1800/t. New Time = t + 3. New Speed = 1800/(t+3).
• Translate the problem's main condition into a mathematical equation. Here, the condition is that the difference in speeds is 300 km/h: (Original Speed) - (New Speed) = 300.
• Solve the resulting algebraic equation for 't'. This may involve simplifying fractions and solving a quadratic equation.
• Evaluate the solution(s) in the context of the problem. Discard any non-physical answers, such as negative time.

Concept Tested & Keywords

• Concept Tested: Solving word problems involving the relationship between time, speed, and distance using algebraic equations.
• Stem keywords: flight, 1800 km, average speed, reduced by 300 km/h, time of flight, increased by 3 hours, original duration
• Lead-in keywords: What was

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