Question

Two trains are moving in opposite directions at a speed of 50 and 70 km/hr. Their lengths are 150m and 100m. The time required for their crossing each other is?

Answer 1

To find the time required for two trains moving in opposite directions to cross each other, we need to do the following steps:

1. **Calculate the relative speed of the trains**:
Since the trains are moving in opposite directions, we add their speeds.
- Speed of train 1 = 50 km/hr
- Speed of train 2 = 70 km/hr

Relative speed = 50 km/hr + 70 km/hr = 120 km/hr

2. **Convert relative speed from km/hr to m/s**:
We use the conversion factor \(1 \text{ km/hr} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s}\).

\[
\text{Relative speed in m/s} = 120 \times \frac{5}{18} = \frac{600}{18} = 33.33 \text{ m/s}
\]

3. **Calculate the total distance to be covered when the trains cross each other**:
The total distance is the sum of the lengths of both trains.
- Length of train 1 = 150 m
- Length of train 2 = 100 m

Total distance = 150 m + 100 m = 250 m

4. **Calculate the time taken to cross each other**:
Using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
\[
\text{Time} = \frac{250 \text{ m}}{33.33 \text{ m/s}} \approx 7.5 \text{ seconds}
\]

Thus, the time required for the two trains to cross each other is approximately **7.5 seconds**.