Question
A train can cross a bridge and a pole in 9 seconds and 6
seconds respectively. The length of the bridge is 90 metres. Find the time taken by train to cross a van which is running in the same direction with a speed of 15 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 + 90) / y} = 9.................(I)
When it crosses the pole,
Or, (x / y) = 6
So, x = 6y............(II)
Or, 6y + 90 = 9y
Or, 90 = 3y
So, y = (90 / 3) = 30 m/sec
And x = 30 × 6 = 180 metres
So, relative speed of the train w.r.t. the van = 30 - 15 = 15 m/sec
So, required time = (180 / 15) = 12 seconds
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