Question
A train can cross a bridge and a pole in 9 seconds and 5 seconds respectively. The length of the bridge is 80 metres. Find the time taken by train to cross a bike which is running in the same direction with a speed of 10 m/sec.
Solution
Let the length and the speed of the train be 'x' metres and 'y' m/sec respectively. When it crosses the bridge, Or, {(x + 80) /y} = 9.................(I) When it crosses the pole, Or, (x/y) = 5 So, 'x' = 5y............(II) Or, 5y + 80 = 9y Or, 80 = 4y So, 'y' = (80/4) = 20 m/sec And 'x' = 20 X 5 = 100 metres So, relative speed of the train w.r.t. the bike = 20 - 10 = 10 m/sec So, required time = (100/10) = 10 seconds
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