The length of train is 120 meters
The speed of train is 25 meter per second
<u><em>Solution:</em></u>
The speed is given by formula:
![speed = \frac{distance}{time}](https://tex.z-dn.net/?f=speed%20%3D%20%5Cfrac%7Bdistance%7D%7Btime%7D)
Given that,
It takes a train 60 seconds to completely drive through a bridge of 1260 m
And 90 seconds to completely drive through a tunnel of 2010 m
Let the length of the train be "x"
<em><u>The total distance travelled by the train across the bridge is given by:</u></em>
total distance = x + 1260 + x = 2x + 1260
[ here we use x + x to represent that train completely drives through bridge ]
The time taken is given as 60 seconds
<em><u>Therefore, the speed is given as:</u></em>
![speed = \frac{2x+ 1260}{60}](https://tex.z-dn.net/?f=speed%20%3D%20%5Cfrac%7B2x%2B%201260%7D%7B60%7D)
<em><u>The total distance travelled by the train through the tunnel is given by:</u></em>
total distance = x + 2010 + x = 2x + 2010
The time taken is given as 90 seconds
<em><u>Therefore, the speed is given as:</u></em>
![speed = \frac{2x+ 2010}{90}](https://tex.z-dn.net/?f=speed%20%3D%20%5Cfrac%7B2x%2B%202010%7D%7B90%7D)
The speed of the train was the same in both cases.
Equate both speeds
![\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B%201260%7D%7B60%7D%20%3D%20%5Cfrac%7B2x%2B%202010%7D%7B90%7D)
![\frac{x+630}{30} = \frac{x+1005}{45}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B630%7D%7B30%7D%20%3D%20%5Cfrac%7Bx%2B1005%7D%7B45%7D)
![45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120](https://tex.z-dn.net/?f=45%28x%2B630%29%20%3D%2030%28x%2B1005%29%5C%5C%5C%5C45x%20%2B%2028350%20%3D%2030x%20%2B%2030150%5C%5C%5C%5C45x%20-%2030x%20%3D%2030150%20-%2028350%5C%5C%5C%5C15x%20%3D%201800%5C%5C%5C%5Cx%20%3D%20120)
Thus length of train is 120 meters
<em><u>Find the speed of train:</u></em>
![speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25](https://tex.z-dn.net/?f=speed%20%3D%20%5Cfrac%7B2x%2B%201260%7D%7B60%7D%5C%5C%5C%5Cspeed%20%3D%20%5Cfrac%7B2%28120%29%20%2B%201260%29%7D%7B60%7D%5C%5C%5C%5Cspeed%20%3D%2025)
Thus speed of train is 25 meter per second