Multiple choice

It takes 15 seconds for a train travelling at 60 km/hr to cross entirely another train half its length and travelling in opposite direction at 48 km/hr. It also passes a bridge in 51 seconds. The length of the bridge is:

  1. 550 m

  2. 450 m

  3. 500 m

  4. 600 m
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A Correct answer
Explanation

Relative speed = 60 + 48 = 108 km/hr = 30 m/s. Let train lengths be L and L/2. Total distance = 1.5L. 1.5L = 30 * 15 = 450, so L = 300. Train 1 speed = 60 km/hr = 50/3 m/s. Passing bridge: (300 + Bridge) = (50/3) * 51 = 850. Bridge = 550 m.

AI explanation

First, convert the speeds to meters per second to get 50/3 m/s and 40/3 m/s. Using the relative speed formula for opposite directions, add the speeds to get 30 m/s. Let the first train's length be L; the second train's length is L/2, making the total distance to cross 3L/2. Dividing this distance by 30 m/s gives 15 seconds, so 3L/2 equals 450, which means L is 300 meters. The total distance to cross the bridge is the train's length plus the bridge's length, which is found by multiplying the train's speed of 50/3 m/s by 51 seconds to get 850 meters. Subtracting the 300 meter train length gives a bridge length of 550 meters.

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