Question

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. How fast does the train travel? What is the length of the train?

Answer 1

The length of train is 120 meters

The speed of train is 25 meter per second

Solution:

The speed is given by formula:

`speed = (distance)/(time)`

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:

`speed = (2x+ 1260)/(60)`

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:

`speed = (2x+ 2010)/(90)`

The speed of the train was the same in both cases.

Equate both speeds

`(2x+ 1260)/(60) = (2x+ 2010)/(90)`

`(x+630)/(30) = (x+1005)/(45)`

`45(x+630) = 30(x+1005)\\\\45x + 28350 = 30x + 30150\\\\45x - 30x = 30150 - 28350\\\\15x = 1800\\\\x = 120`

Thus length of train is 120 meters

Find the speed of train:

`speed = (2x+ 1260)/(60)\\\\speed = (2(120) + 1260))/(60)\\\\speed = 25`

Thus speed of train is 25 meter per second