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 - 28 August 2019 (Shift-1)

Explanation

• The problem is solved by setting up two equations based on the formula Distance = Speed × Time, one for the original journey and one for the journey under new conditions.
• Substituting one equation into the other results in a quadratic equation: t² + 3t - 18 = 0, where 't' is the original time.
• Factoring the quadratic equation gives (t + 6)(t - 3) = 0.
• The possible solutions are t = 3 and t = -6. Since time cannot be negative, the only valid solution is 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 60 km/h. The distance covered would be 8 * 60 = 480 km, not 1800 km.
• 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 150 km/h. The distance covered would be 7 * 150 = 1050 km, not 1800 km.
• Option D: If the original time was 6 hours, the original speed would be 1800/6 = 300 km/h. The new speed would be 300 - 300 = 0 km/h, which is illogical as the flight would not be moving. The calculated new distance would be 0 km.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving mathematical word problems involving the relationship between speed, distance, and time, often leading to the formation and solution of a quadratic equation as background academic context rather than a clinical decision trigger.
• This question tests mathematical aptitude and problem-solving skills, which are essential for nursing practice.
• While not a direct clinical question, the logical reasoning required is similar to that used in calculating drug dosages, IV drip rates, and interpreting patient data trends.
• For example, a nurse needs to calculate the infusion time for a certain volume of fluid at a specific rate, which uses the same fundamental principles (Volume = Rate × Time).

How to Approach the Question

• First, carefully read the problem and identify all the given numerical values and the relationships between them (e.g., speed reduced by X, time increased by Y).
• Define variables for the unknown quantities you need to find. In this case, the original speed (s) and original time (t).
• Use the fundamental formula (Distance = Speed × Time) to create equations that model the situation described in the problem. You will likely have one equation for the 'original' state and one for the 'new' state.
• Combine the equations through substitution or elimination to create a single equation with one variable.
• Solve the resulting equation. In this case, it's a quadratic equation. Remember to check for extraneous solutions (like negative time) that don't make sense in the context of the problem.
• Once you have a valid answer, you can plug it back into the original problem to verify that it works.

Concept Tested & Keywords

• Concept Tested: Solving mathematical word problems involving the relationship between speed, distance, and time, often leading to the formation and solution of a quadratic equation.
• Stem keywords: flight, 1800 km, slowed down, average speed, reduced by 300 km/h, time of flight, increased by 3 hours
• Lead-in keywords: What was, original duration

Question ID

Q4BnAOdwkY-kHYhZ6c4_iQ

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