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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Important Questions from Relative Speed
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- X and Yrun a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
A train of length 600 meters passes another train of length 1000 meters moving in the opposite direction in 96 seconds. If the speed of both the trains is the same, then what is the speed of each train?
The distance between Delhi and Patna is $480$ km. A train starts from Delhi and travels towards Patna at a speed of $60$ kmph. Another train starts from Patna towards Delhi at a speed of $80$ kmph, but starts $1$ hour after the first train. In how much time, after the first train started, will they meet each other?
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