A train passes a station platform in 69 seconds and a man standing on the platform in 53 seconds. If the speed of the train is $29\mathrm{m/s}$, what is the length of the platform? (meter)

1. A

   464

2. B

   494

3. C

   484

4. D

   474

Appeared in: RRB Nsg. Superintendent-20 July 2019 (Shift-3rd)

Explanation

• The time a train takes to pass a stationary point (a man) is the time required to cover its own length.
• The time a train takes to pass a platform is the time required to cover its own length plus the length of theplatform.
• The difference between these two times (69s - 53s = 16s) represents the exact time taken to cover the length of the platform alone.
• Multiplying this time difference by the train's speed gives the platform's length: 16 s × 29 m/s = 464 meters.

Why Other Options Were Wrong

• Option B: This value is an incorrect result of the calculation. It may arise from a miscalculation of the product of the time difference (16s) and the speed (29 m/s). For instance, incorrectly calculating 17 x 29 = 493, which is close to 494.
• Option C: This value is an incorrect result of the calculation. It could be the result of rounding the speed or time before multiplying. For example, rounding the speed to 30 m/s would give 16 s * 30 m/s = 480 m, which is close to 484.
• Option D: This value is an incorrect result of the calculation. It does not correspond to the correct multiplication of the time difference (16s) and the speed (29 m/s).

Related Visual

• Visual 1: Diagram - A visual showing two scenarios. Scenario 1: A train of length 'L_t' passing a stationary man. The total distance covered is L_t. Scenario 2: The same train passing a platform of length 'L_p'. The total distance covered is the sum of the train's length and the platform's length (L_t + L_p). This helps clarify why the time taken is longer for the platform.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating distance based on speed and time in relative motion problems involving trains and platforms as background academic context rather than a clinical decision trigger.
• This question tests quantitative aptitude and logical reasoning, which are foundational skills for problem-solving in various professional fields.
• While not directly clinical, the ability to perform accurate calculations is crucial in nursing for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data.
• What if? - If the train's speed was 30 m/s instead of 29 m/s, the length of the platform would be the time difference (16s) multiplied by the new speed: 16 s × 30 m/s = 480 meters.

How to Approach the Question

• Step 1: Identify all the given information: Speed of the train (S = 29 m/s), time to pass the platform (T_p = 69 s), and time to pass the man (T_m = 53 s).
• Step 2: Understand the underlying concepts. The distance covered when passing a man is the train's length. The distance covered when passing a platform is the train's length plus the platform's length.
• Step 3: Find the difference in time taken for both events. This time difference (T_p - T_m) corresponds to the time taken to cover the length of the platform.
• Step 4: Calculate the time difference: 69 seconds – 53 seconds = 16 seconds.
• Step 5: Apply the distance formula (Distance = Speed × Time) to find the length of the platform. Multiply the time difference by the train's speed.
• Step 6: Perform the calculation: Length of Platform = 29 m/s × 16 s = 464 meters. Select the corresponding option.

Concept Tested & Keywords

• Concept Tested: Calculating distance based on speed and time in relative motion problems involving trains and platforms.
• Stem keywords: train, station platform, man standing, speed, length of the platform
• Lead-in keywords: what is

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QN6YWhALqnoUcTN9FvQRWs

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