Solving Train Meeting Time Problem

This problem requires calculating the time it takes for two trains, moving in opposite directions, to completely pass each other after they meet.

Key Information

• Train 1 Length ($L_1$): 136 m
• Train 2 Length ($L_2$): 185 m
• Train 1 Speed ($S_1$): 70 km/h
• Train 2 Speed ($S_2$): 65 km/h
• Direction: Opposite

Calculations

1. Determine the total distance needed for the trains to clear each other. This is the sum of their lengths:

   Total Length ($L$) = $L_1 + L_2$

   $L = 136 \text{ m} + 185 \text{ m} = 321 \text{ m}$

2. Calculate the relative speed ($S_{rel}$) of the two trains. Since they are moving in opposite directions, their speeds add up:

   $S_{rel} = S_1 + S_2$

   $S_{rel} = 70 \text{ km/h} + 65 \text{ km/h} = 135 \text{ km/h}$

3. Convert the relative speed from kilometers per hour (km/h) to meters per second (m/s) for consistency with the length unit:

   $S_{rel} (\text{m/s}) = S_{rel} (\text{km/h}) \times \frac{5}{18}$

   $S_{rel} = 135 \times \frac{5}{18} = 37.5 \text{ m/s}$

4. Calculate the time ($t$) required for the trains to clear each other using the formula: Time = Total Distance / Relative Speed:

   $t = \frac{L}{S_{rel}}$

   $t = \frac{321 \text{ m}}{37.5 \text{ m/s}}$

   $t = 8.56 \text{ s}$

Result

The time required for the two trains to completely clear each other is 8.56 seconds.