Two trains, 120m and 180m long, are running in opposite directions on parallel tracks at speeds of 40 km/h and 50 km/h, respectively. How long will they take to cross each other?

1. A

   10 seconds

2. B

   12 seconds

3. C

   15 seconds

4. D

   20 seconds

Appeared in: DSSSB 6 September 2024

Explanation

• To find the crossing time, you must calculate the total distance and the relative speed of the trains.
• The total distance is the sum of the lengths of both trains: 120 m + 180 m = 300 m.
• Since the trains are moving in opposite directions, their relative speed is the sum of their individual speeds: 40 km/h + 50 km/h = 90 km/h.
• The speed must be converted to meters per second (m/s) to match the unit of distance. This is done by multiplying by 5/18: 90 km/h × (5/18) = 25 m/s.
• The time taken is calculated by dividing the total distance by the relative speed: Time = 300 m / 25 m/s = 12 seconds.

Why Other Options Were Wrong

• Option A: Calculating the time as 10 seconds would imply a relative speed of 30 m/s (300 m / 10 s), which is 108 km/h. The actual relative speed is 90 km/h.
• Option C: Calculating the time as 15 seconds would imply a relative speed of 20 m/s (300 m / 15 s), which is 72 km/h. The actual relative speed is 90 km/h.
• Option D: Calculating the time as 20 seconds would imply a relative speed of 15 m/s (300 m / 20 s), which is 54 km/h. The actual relative speed is 90 km/h.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Relative speed calculation for objects moving in opposite directions as background academic context rather than a clinical decision trigger.
• This question tests general intelligence and quantitative aptitude, which are essential problem-solving skills for nurses.
• Accurate calculation skills are critical in nursing for tasks like medication dosage, IV drip rate calculations, and interpreting patient data.
• What if? If the trains were moving in the same direction, the relative speed would be the difference (50 - 40 = 10 km/h). The time to cross would be much longer: 300 m / (10 × 5/18 m/s) = 108 seconds.

How to Approach the Question

• First, identify the given information: the lengths of both trains and their respective speeds.
• Recognize that the 'total distance' to be covered for one train to completely cross the other is the sum of their lengths.
• Determine the rule for 'relative speed'. Since the trains are moving in opposite directions, their speeds must be added together.
• Ensure all units are consistent. Convert the speed from km/h to m/s to match the distance in meters using the conversion factor 5/18.
• Apply the fundamental formula: Time = Total Distance / Relative Speed.
• Perform the final calculation and select the matching option.

Concept Tested & Keywords

• Concept Tested: Relative speed calculation for objects moving in opposite directions.
• Stem keywords: trains, 120m, 180m, opposite directions, 40 km/h, 50 km/h
• Lead-in keywords: How long

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Q9z9Ini5CoeSM9bvH8pgo1

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