Question
Two trains of equal lengths takes 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 miters, in what time ( in seconds) will they cross each other traveling in opposite direction?
Answer: Option B
$$\eqalign{
& {\text{Speed of the train}} \cr
& {\text{ = }}\left( {\frac{{120}}{{10}}} \right){\text{ m/sec}} \cr
& {\text{ = 12 m/sec}} \cr
& {\text{Speed of the second train}} \cr
& {\text{ = }}\left( {\frac{{120}}{{15}}} \right){\text{ m/sec}} \cr
& {\text{ = 8 m/sec}} \cr
& {\text{Relative speed}} \cr
& {\text{ = (12 + 8)m/sec}} \cr
& {\text{ = 20 m/sec}} \cr
& \therefore {\text{Required time}} \cr
& {\text{ = }}\frac{{\left( {120 + 120} \right)}}{{20}}\,\sec \cr
& = 12\,\sec \cr} $$
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$$\eqalign{
& {\text{Speed of the train}} \cr
& {\text{ = }}\left( {\frac{{120}}{{10}}} \right){\text{ m/sec}} \cr
& {\text{ = 12 m/sec}} \cr
& {\text{Speed of the second train}} \cr
& {\text{ = }}\left( {\frac{{120}}{{15}}} \right){\text{ m/sec}} \cr
& {\text{ = 8 m/sec}} \cr
& {\text{Relative speed}} \cr
& {\text{ = (12 + 8)m/sec}} \cr
& {\text{ = 20 m/sec}} \cr
& \therefore {\text{Required time}} \cr
& {\text{ = }}\frac{{\left( {120 + 120} \right)}}{{20}}\,\sec \cr
& = 12\,\sec \cr} $$
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