A man completes a journey in 16 hours. He travels the first half of the journey at 16 km/h and the second half at 24 km/h. Find the total journey distance.

1. A

   302.5 km

2. B

   307.2 km

3. C

   311.4 km

4. D

   308.8 km

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

• The core principle is Time = Distance / Speed.
• Let the total distance be D. The time for the first half is (D/2)/16 = D/32 hours.
• The time for the second half is (D/2)/24 = D/48 hours.
• The total time is 16 hours, so the governing equation is D/32 + D/48 = 16.
• Solving this equation: (3D + 2D)/96 = 16, which simplifies to 5D = 16 * 96.
• This gives D = 1536 / 5, which equals 307.2 km.

Why Other Options Were Wrong

• Option A: This value is incorrect. It likely results from a miscalculation when finding the common denominator or solving the final equation for the distance D.
• Option C: This value is incorrect. It is a result of an arithmetic error during the calculation process, possibly in the multiplication or division steps.
• Option D: This value is incorrect. Such an error could occur if the relationship between time, speed, and distance is set up improperly in the initial equation.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of total distance based on time and variable speeds over equal segments of a journey as background academic context rather than a clinical decision trigger.
• This question assesses quantitative aptitude, a skill often included in the non-nursing, general intelligence sections of nursing and other competitive examinations.
• Proficiency in solving such problems demonstrates logical reasoning and mathematical ability, which are important for a variety of analytical tasks.
• What if? - If the man traveled for two equal time periods (8 hours each) at these speeds instead of equal distances, the calculation would be simpler. The total distance would be (8 hours × 16 km/h) + (8 hours × 24 km/h) = 128 + 192 = 320 km.

How to Approach the Question

• First, identify all the given information: total time (16 hours), speed for the first half (16 km/h), and speed for the second half (24 km/h).
• Recognize that the journey is split into two equal distances.
• Assign a variable for the unknown total distance, such as 'D'. This makes the distance of each half D/2.
• Use the fundamental formula Time = Distance / Speed to write expressions for the time taken for each half of the journey.
• Create an equation by summing the time for both halves and setting it equal to the total given time (16 hours).
• Solve the resulting algebraic equation for 'D' to find the total distance.

Concept Tested & Keywords

• Concept Tested: Calculation of total distance based on time and variable speeds over equal segments of a journey.
• Stem keywords: journey, 16 hours, first half, 16 km/h, second half, 24 km/h, total journey distance
• Lead-in keywords: Find

Question ID

QXSTMnyW0E6fIYpwm5uR0D

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