Question
A train can cross a bridge and a pole in 7.5 seconds and 5
seconds respectively. The length of the bridge is 50 metres. Find the time taken by train to cross a man who 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 + 50) / y} = 7.5.................(I)
When it crosses the pole,
Or, (x / y) = 5
So, x = 5y............(II)
Or, 5y + 50 = 7.5y
Or, 50 = 2.5y
So, y = (50 / 2.5) = 20 m/sec
And x = 20 × 5 = 100 metres
So, relative speed of the train w.r.t. the man = 20 - 10 = 10 m/sec
So, required time = (100 / 10) = 10 seconds
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