Running at a speed of 60 km per hour, a train passed through a 1-5 km long tunnel in two minutes. What is the length of the train

Explanation

We can start by converting the speed of the train from km/h to m/s. 60 km/h = (60 x 1000) / (60 x 60) m/s = 16.67 m/s We know that the train takes 2 minutes to pass through the tunnel, which is equivalent to 120 seconds. Let`s assume that the length of the train is `x`. When the train enters the tunnel, it takes time `t1` to completely enter the tunnel. Similarly, when the train exits the tunnel, it takes time `t2` to completely exit the tunnel. The total time taken by the train to pass through the tunnel is t1 + t2. We can use the formula: distance = speed x time to calculate the distance travelled by the train during t1 and t2. During t1, the train travels a distance equal to the length of the tunnel + the length of the train. During t2, the train travels a distance equal to the length of the train. Therefore, we can write the equation: 1.5 + x = 16.67 x t1 (distance = speed x time) x = 16.67 x t2 (distance = speed x time) We know that t1 + t2 = 120 seconds. Substituting the second equation into the first equation, we get: 1.5 + (16.67 x t2) = 16.67 x (120 – t2) Solving for t2, we get: t2 = 30 seconds Substituting t2 back into the second equation, we get: x = 16.67 x 30 = 500 meters Therefore, the length of the train is 500 meters. Answer: 500 meters.