Two trains of lengths 155 m and 160 m are running at speeds of 74 km/hr and 52 km/hr, respectively, on parallel tracks in opposite directions. In how many seconds will they pass each other?
9 seconds
To determine how many seconds the two trains will take to pass each other, we need to follow these steps:
- First, convert the speeds of both trains from km/hr to m/s to ensure consistency with the lengths provided in meters.
- Speed of the first train: \(74 \text{ km/hr} = \frac{74 \times 1000}{3600} \text{ m/s} = \frac{74000}{3600} \text{ m/s} = \frac{370}{18} \text{ m/s} \approx 20.56 \text{ m/s}\)
- Speed of the second train: \(52 \text{ km/hr} = \frac{52 \times 1000}{3600} \text{ m/s} = \frac{52000}{3600} \text{ m/s} = \frac{130}{9} \text{ m/s} \approx 14.44 \text{ m/s}\)
- The trains are moving in opposite directions, so we add their speeds to find the relative speed:
- Total relative speed = \(20.56 \text{ m/s} + 14.44 \text{ m/s} = 35 \text{ m/s}\)
- To find the time taken to cross each other, calculate the total distance covered, which is the sum of the lengths of the trains:
- Total distance = \(155 \text{ m} + 160 \text{ m} = 315 \text{ m}\)
- Finally, use the formula: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) to find the crossing time:
- \(\text{Time} = \frac{315 \text{ m}}{35 \text{ m/s}} = 9 \text{ seconds}\)
Therefore, the trains will pass each other in 9 seconds, which confirms the correct answer option is 9 seconds.
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