Question
A train can cross a bridge and a pole in 7.2 seconds and 4
seconds respectively. The length of the bridge is 80 metres. Find the time taken by train to cross a car which is running in the same direction with a speed of 20 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} = 7.2.................(I)
When it crosses the pole,
Or, (x / y) = 4
So, x = 4y............(II)
Or, 4y + 80 = 7.2y
Or, 80 = 3.2y
So, y = (80 / 3.2) = 25 m/sec
And x = 25 Ć 4 = 100 metres
So, relative speed of the train w.r.t. the car = 25 - 20 = 5 m/sec
So, required time = (100 / 5) = 20 seconds
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