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 ?
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 ?
(a)
250 m
(b)
500 m
(c)
1000 m
(d)
1500 m
(b)
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.
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