Two trains each of length \(100\text{ m}\) are running on parallel tracks. One overtakes the other in \(20\text{ s}\) when they are moving in the same direction and crosses the other in \(10\text{ s}\) when they move in the opposite directions. The velocities of the two trains are:
\(15\text{ m/s}\) & \(5\text{ m/s}\)
\(25\text{ m/s}\) & \(15\text{ m/s}\)
\(10\text{ m/s}\) & \(10\text{ m/s}\)
\(30\text{ m/s}\) & \(10\text{ m/s}\)
Solution:
Let the velocities be \(v_1\) and \(v_2\). Distance to cross is \(100 + 100 = 200\text{ m}\). For same direction: \(v_1 - v_2 = 200/20 = 10\text{ m/s}\). For opposite direction: \(v_1 + v_2 = 200/10 = 20\text{ m/s}\). Solving these gives \(v_1 = 15\text{ m/s}\) and \(v_2 = 5\text{ m/s}\).
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