Question
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
Answer: Option C
$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{slower}}\,{\text{train}}\,{\text{be}}\,x\,{\text{m/sec}} \cr
& {\text{Then,}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{faster}}\,{\text{train}} = 2x\,{\text{m/sec}} \cr
& {\text{Relative}}\,{\text{speed}} = \,\left( {x + 2x} \right)\,{\text{m/sec}} = 3x\,{\text{m/sec}} \cr
& \therefore \frac{{ {100 + 100} }}{8} = 3x \cr
& \Rightarrow 24x = 200 \cr
& \Rightarrow x = \frac{{25}}{3} \cr
& {\text{So,}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{faster}}\,{\text{train}}\, = \frac{{50}}{3}\,{\text{m/sec}} \cr
& = {\frac{{50}}{3} \times \frac{{18}}{5}} \,{\text{km/hr}} \cr
& = 60\,{\text{km/hr}} \cr} $$
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$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{slower}}\,{\text{train}}\,{\text{be}}\,x\,{\text{m/sec}} \cr
& {\text{Then,}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{faster}}\,{\text{train}} = 2x\,{\text{m/sec}} \cr
& {\text{Relative}}\,{\text{speed}} = \,\left( {x + 2x} \right)\,{\text{m/sec}} = 3x\,{\text{m/sec}} \cr
& \therefore \frac{{ {100 + 100} }}{8} = 3x \cr
& \Rightarrow 24x = 200 \cr
& \Rightarrow x = \frac{{25}}{3} \cr
& {\text{So,}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{faster}}\,{\text{train}}\, = \frac{{50}}{3}\,{\text{m/sec}} \cr
& = {\frac{{50}}{3} \times \frac{{18}}{5}} \,{\text{km/hr}} \cr
& = 60\,{\text{km/hr}} \cr} $$
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