The problem asks for the time it takes for two trains moving in opposite directions to completely pass each other.
Calculating Train Passing Time
1. Convert Speeds to Meters per Second (m/s)
The speeds are given in km/h, but the lengths are in meters and the required time is in seconds. We need to convert the speeds using the factor $\frac{5}{18}$.
- Speed of Z1 Express ($S_1$): $149 \text{ km/h} = 149 \times \frac{5}{18} \text{ m/s}$
- Speed of X1 Express ($S_2$): $139 \text{ km/h} = 139 \times \frac{5}{18} \text{ m/s}$
2. Calculate Relative Speed
When two objects move in opposite directions, their relative speed is the sum of their individual speeds.
Relative Speed ($S_{rel}$) = $S_1 + S_2$
$S_{rel} = \left( 149 \times \frac{5}{18} \right) + \left( 139 \times \frac{5}{18} \right) \text{ m/s}$ $S_{rel} = (149 + 139) \times \frac{5}{18} \text{ m/s}$ $S_{rel} = 288 \times \frac{5}{18} \text{ m/s}$ $S_{rel} = 16 \times 5 \text{ m/s}$ $S_{rel} = 80 \text{ m/s}$3. Calculate Total Relative Distance
For the trains to pass each other completely, the total distance covered relative to each other is the sum of their lengths.
Length of Z1 Express ($L_1$) = 755 m
Length of X1 Express ($L_2$) = 685 m
Total Relative Distance ($D_{rel}$) = $L_1 + L_2$
$D_{rel} = 755 \text{ m} + 685 \text{ m}$ $D_{rel} = 1440 \text{ m}$4. Calculate Time to Pass
The time taken is the total relative distance divided by the relative speed.
Time ($T$) = $\frac{D_{rel}}{S_{rel}}$
$T = \frac{1440 \text{ m}}{80 \text{ m/s}}$ $T = 18 \text{ seconds}$Important Questions from Problem on Trains
- A train with a length of 195 m overtakes a man moving at a speed of 5 km/hr (in the same direction) in 13 seconds. How much time (in seconds) will it take this train to completely cross another train that is 255 m long, moving in the opposite direction at a speed of 76 km/hr?
- Train A leaves station M at 8:25 AM and reaches station N at 3:25 PM on the same day. Train B leaves station N at 10:25 AM and reaches station M at 3:25 PM on the same day. Find the time when trains A and B meet.
- A train of length 490 m overtakes a man moving at a speed of 9 km/hr (in the same direction) in 12 seconds. How much time (in seconds) will it take this train to completely cross another train that has is 500 m long, moving in the opposite direction at a speed of 42 km/hr?
- Train A leaves station M at 7:55 a.m. and reaches station N at 2:55 p.m. on the same day. Train B leaves station N at 9:55 a.m. and reaches station M at 2:55 p.m. on the same day. Find the time when Trains A and B meet.
Train A leaves station M at 6:40 AM and reaches station N at 3:40 PM on the same day. Train B leaves station N at 8:40 AM and reaches station M at 2:40 PM on the same day. Find the time when trains A and B meet.
