(1) Two trains of equal length and moving with the same speed of 54 km/h in opposite directions cross each other in 10 sec. Find the length of the trains.
(2) The speed of a boat in still water is 8 km/h. If the boat covers a distance of 16.5 km upstream in 3 hours, find the speed of the current.
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2015-06-18T20:46:23+05:30

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   2 * length / (54+54) = 10 / 3600
    =>  length = 108 * 10 / 7200 = 0.15 km = 150 meters

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Length = L meters.
The trains are moving with constant speed = v = 54 km/h = 54  * 5/18 = 15 m/sec

We use the concept of relative velocity.  Let us view from the reference of one train.  With respect to a person on one train, the other train is travelling with twice the speed = 15 + 15 = 30 m/sec.

The distance to be travelled is 2 * train length = 2 * L meters.

Hence, the time taken = distance / speed = 2 L / 30  = 10 sec
       =>  L = 150 meters.
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2)
     Speed of boat = V = 8 km/hr
     velocity of current in river = R  km/hr

when a boat travels upstream its velocity = V - R = (8 - R)  km/h

   distance covered = speed * time duration
     =>   16.5 km = (8 - R) * 3 hours
     =>  8 - R = 16.5/3 = 5.5 km/hr
                   R = 2.5 km/h

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