It took a train 50 seconds to pass a tunnel that was 1000m long. It took the same train, travelling at the same speed, 75 seconds to pass a Bridge that was 1625m long. How long was the train?
Answers
The length of the train passing a 1000 m tunnel in 50 secs and a 1625 m bridge in 75 sec is 125 m.
Explanation:
Let the length of the train be “x” m.
In the question, we can see that the train completely crosses a tunnel and also a bridge, so here we can say that passing a tunnel or a bridge can be interpreted as the train enters the tunnel or the bridge, and completely leaves the same.
It is given that,
The length of the tunnel = 1000 m
Time taken to completely pass the tunnel = 50 secs
∴ The total distance that the train covered while passing the tunnel will be,
= x + 1000 + x
= (2x + 1000) m
And
The speed of the train while passing the tunnel will be,
= Distance/Time
= [2x+1000] / 50 …… (i)
Also given,
The length of the bridge = 1625 m
Time taken to completely pass the tunnel = 75 secs
∴ The total distance that the train covered while passing the bridge will be,
= x + 1625 + x
= (2x + 1625) m
And
The speed of the train while passing the bridge will be,
= Distance/Time
= [2x+1625] / 75 …… (ii)
Since it is given in the question that the speed of the train is the same in both the cases, therefore, we can equate both the eq. (i) & (ii),
[2x+1000] / 50 = [2x+1625] / 75
⇒ [2x+1000] / 2 = [2x+1625] / 3
⇒ 6x + 3000 = 4x + 3250
⇒ 2x = 250
⇒ x = 250/2
⇒ x = 125 m
Thus, the length of the train will be 125 meters.
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