Two trains of equal lengths cross a stationary pole in 12 seconds and 16 seconds, respectively. How long will it take for the trains to cross each other when running in opposite directions? (Write your answer rounded off to two decimal places.)
13.71 seconds
Since both trains have the same length L, their speeds are \(\tfrac{L}{12}\) and \(\tfrac{L}{16}\).
Crossing time in opposite directions: \(\dfrac{2L}{L/12+L/16} = \dfrac{2}{1/12+1/16}\).
\(\dfrac1{12}+\dfrac1{16} = \dfrac{4}{48}+\dfrac{3}{48} = \dfrac{7}{48}\), so time \(=\dfrac{2}{7/48} = \dfrac{96}{7} \approx 13.71\).
Hence, the trains take approximately 13.71 seconds to cross each other.
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