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A train passes two bridges of lengths $ 210 \mathrm{~m} $ and $ 122 \mathrm{~m} $ in 25 sec and 17 sec respectively. Calculate the length and speed of the train.
Given:
A train passes two bridge of lengths \( 210 \mathrm{~m} \) and \( 122 \mathrm{~m} \) in 25 sec and 17 sec respectively.
To do:
We have to find the length and speed of the train.
Solution:
Let the length of the train be $x$.
In both cases, the speed of the train is the same.
This implies,
It travels $(210+x)\ m$ in 25 sec and $(122+x)\ m$ in 17 sec.
We know that,
$Speed = \frac{Distance}{Time}$
Therefore,
$\frac{210 + x}{25} = \frac{122+x}{17}$
$17(210 + x) = 25(122 + x)$ (On cross multiplication)
$3570+17x=3050+25x$
$3570-3050 = 25x-17x$
$520=8x$
$x=\frac{520}{8}$
$x = 65\ m$
Therefore, the length of the train is 65 m.
$Speed = \frac{210+65}{25}$
$=\frac{275}{25}$
$= 11\ m/s$
The length of the train is 65 m and the speed of the train is 11 m/s.
Updated on: 10-Oct-2022
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