To find the time required for two trains moving in opposite directions to cross each other, we need to do the following steps:
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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
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Convert relative speed from km/hr to m/s: We use the conversion factor \(1 \text{ km/hr} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s}\).
\[ \text{Relative speed in m/s} = 120 \times \frac{5}{18} = \frac{600}{18} = 33.33 \text{ m/s} \]
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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
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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.
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