Two Trains Crossing
When two trains cross each other, you must track both their combined lengths and their relative speeds. Whether they are traveling toward each other or moving in the same direction, the total distance to complete the passing is always the sum of both train lengths.
Fundamental Principles
Combined Train Spatial Footprint
The total physical distance that must be cleared during an intersection, calculated as: $\text{Total Distance} = \text{Length of Train 1} + \text{Length of Train 2}$.
Essential Formulation Tips
- The total distance value is always the sum of both lengths ($L_1 + L_2$), regardless of which direction the trains are moving.
- Always calculate your relative speed first based on directional paths before setting up the time equation.
Shortcut Execution Techniques
- The Overtake Shortcut: When a faster train overtakes a slower train moving in the same direction, the relative speed is simply the difference between their speeds, while the distance remains the sum of their lengths.
Contextual Inquiries (FAQs)
Q: Do we ever subtract train lengths if they are traveling in the same direction?
A: No. Lengths are always added together because the total distance required for one train to completely pass through the physical footprint of another never changes.
Example Breakdown: Calculating Opposite-Direction Crossing Times
Standard opposite direction dual train crossing example.Calculate the total distance: $\text{Distance} = L_1 + L_2 = 100\text{m} + 150\text{m} = 250 \text{ meters}$.
Determine the relative motion path: They are moving toward each other (opposite directions), so add their speeds together.
Calculate relative speed: $\text{Relative Speed} = 54 \text{ km/h} + 36 \text{ km/h} = 90 \text{ km/h}$.
Convert relative speed to m/s: $90 \times \frac{5}{18} = 25 \text{ m/s}$.
Apply the time equation: $\text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}}$
Perform final division: $\text{Time} = \frac{250}{25} = 10 \text{ seconds}$.
Conclusion: The trains pass each other completely in 10 seconds.
Dual Moving Train Crossing Drills
Practice calculating cross-over times for parallel tracks under different directional rules.
Q1. Two trains of lengths 120 meters and 80 meters run in the same direction on parallel tracks at 70 km/h and 52 km/h. How many seconds will it take the faster train to completely pass the slower one?