A man traveled from his village to the post office at a speed of 25km/hr and returned at a speed of 4km/hr. If the entire journey took 5 hours and 48 minutes, the distance from his village to the post office is:

1. A

   20km

2. B

   40km

3. C

   30km

4. D

   35km

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

• The core relationship used is Time = Distance / Speed.
• The total time for the round trip is the sum of the time taken for each leg of the journey.
• First, convert the total time into a single unit (hours): 5 hours 48 minutes = 5 + (48/60) = 5.8 hours.
• Set up the equation representing the total time: (Distance/25) + (Distance/4) = 5.8.
• Solving this equation for the distance (d) gives (4d + 25d)/100 = 5.8, which simplifies to 29d = 580.
• The final calculation yields a one-way distance (d) of 20 km.

Why Other Options Were Wrong

• Option B: This value represents the total distance for the entire round trip (20 km to the post office and 20 km back), not the one-way distance from the village to the post office that the question asks for.
• Option C: This value is incorrect and would result from a miscalculation, such as an error in converting the time or an arithmetic mistake while solving the algebraic equation.
• Option D: This value is incorrect and likely stems from a calculation error, either in setting up the initial equation or during the algebraic manipulation to solve for the distance.

Related Visual

• Visual 1: Diagram - A simple diagram showing a path from a 'Village' to a 'Post Office'. An arrow pointing from the village to the post office is labeled 'Speed = 25 km/hr', and an arrow pointing back is labeled 'Speed = 4 km/hr'. The distance 'd' is marked between them.
• Visual 2: Formula Triangle - A triangle divided into three sections with 'Distance' at the top and 'Speed' and 'Time' at the bottom, illustrating the relationships D = S × T, S = D / T, and T = D / S.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a word problem involving distance, speed, and time for a round trip as background academic context rather than a clinical decision trigger.
• While not a direct clinical skill, understanding these calculations is crucial for logistics in community health nursing, such as planning home visit schedules or managing travel time for outreach programs.
• This type of problem-solving enhances general aptitude and numerical reasoning skills, which are frequently tested in nursing entrance and recruitment examinations.
• What if? If the total time was exactly 6 hours, the equation would be d/25 + d/4 = 6. This would lead to 29d/100 = 6, so d = 600/29, which is approximately 20.69 km. This demonstrates how a small change in time affects the final distance.

How to Approach the Question

• First, identify all the given values: speed for the first part of the journey (s1 = 25 km/hr), speed for the return journey (s2 = 4 km/hr), and the total time taken (T).
• Convert the total time into a single, consistent unit. Here, convert 5 hours and 48 minutes into hours by dividing the minutes by 60 (48/60 = 0.8), giving a total of 5.8 hours.
• Define the unknown variable. Let the one-way distance be 'd'. Since the journey is to a place and back, the distance for both parts is the same.
• Set up an equation using the formula Time = Distance / Speed. The total time is the sum of the time for each part: (d/s1) + (d/s2) = T.
• Substitute the known values into the equation: d/25 + d/4 = 5.8.
• Solve the resulting algebraic equation for 'd' to find the one-way distance.

Concept Tested & Keywords

• Concept Tested: Solving a word problem involving distance, speed, and time for a round trip.
• Stem keywords: traveled, speed, 25km/hr, returned, 4km/hr, journey, 5 hours and 48 minutes, distance
• Lead-in keywords: the distance... is:

Question ID

QbH-nofQbxI2qpF8cwM9o3

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