Respuesta :
The length of train is 120 meters
The speed of train is 25 meter per second
Solution:
The speed is given by formula:
[tex]speed = \frac{distance}{time}[/tex]
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"
The total distance travelled by the train across the bridge is given by:
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
Therefore, the speed is given as:
[tex]speed = \frac{2x+ 1260}{60}[/tex]
The total distance travelled by the train through the tunnel is given by:
total distance = x + 2010 + x = 2x + 2010
The time taken is given as 90 seconds
Therefore, the speed is given as:
[tex]speed = \frac{2x+ 2010}{90}[/tex]
The speed of the train was the same in both cases.
Equate both speeds
[tex]\frac{2x+ 1260}{60} = \frac{2x+ 2010}{90}[/tex]
[tex]\frac{x+630}{30} = \frac{x+1005}{45}[/tex]
[tex]45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120[/tex]
Thus length of train is 120 meters
Find the speed of train:
[tex]speed = \frac{2x+ 1260}{60}\\\\speed = \frac{2(120) + 1260)}{60}\\\\speed = 25[/tex]
Thus speed of train is 25 meter per second
