Question
A train can cross a bridge and a pole in 6 seconds and 3.6
seconds respectively. The length of the bridge is 60 metres. Find the time taken by train to cross a scooter 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 + 60) / y} = 6.................(I)
When it crosses the pole,
Or, (x / y) = 3.6
So, x = 3.6y............(II)
Or, 3.6y + 60 = 6y
Or, 60 = 2.4y
So, y = (60 / 2.4) = 25 m/sec
And x = 25 × 3.6 = 90 metres
So, relative speed of the train w.r.t. the scooter = 25 - 15 = 10 m/sec
So, required time = (90 / 10) = 9 seconds
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