A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?

2 Answers on this Question

1. 9.6 seconds

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2. – While the train is moving, the jogger will also be running in the same direction.
   – for the head(engine) of the train to get to the current position of the jogger 240m away, it will take:
   45km/hr => 12.5m/s => 240/12.5 = 19.2 seconds.

   – But in the same period of time, the jogger will still be running and will have moved to a new location by: 9km/hr => 2.5m/s => 2.5 * 19.2 = 48m

   To get to the new location at the speed of 12.5m/s will take the train:
   48/12.5 = 3.84sec

   In this additional time, the jogger will move forward by:
   3.84 * 2.5 = 9.6m

   at a speed of 12.5m/s, it will take the train less than a second to cover the additional 9.6m

   If we add the distance the jogger will cover in 1 second to 9.6, it is still less than what the train can cover per second. let us see (9.6 + 2.5 = 12.1)

   Therefore, the head of the train will pass the runner at approximately: 19.2 + 3.84 + 1 => 24.04 seconds.

   For the train to completely pass the runner, it will need its whole length of 120m to be in front of the runner.

   This will take an additional (9.6 + 2) seconds.

   Therefore for the length of the train to be ahead of the runner it will take approx. 35.65 (24.04 + 9.6 + 2) seconds

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