A train 100 meters long passes a bridge at the rate of 72 kilometers per hour in 25 seconds. What is the length of the bridge?

Let’s break down the information given:

The train is 100 meters long.
The train passes a bridge.
The train’s speed is 72 kilometers per hour (km/h).
The time taken to pass the bridge is 25 seconds.
First, let’s convert the train’s speed from kilometers per hour to meters per second, since the length of the train is given in meters and the time is given in seconds.

1 kilometer = 1000 meters
1 hour = 3600 seconds

So, the train’s speed in meters per second is:
(72 km/h) * (1000 m/km) / (3600 s/h) = 20 m/s

Now, we can calculate the distance the train travels in 25 seconds at a speed of 20 m/s:
Distance = Speed × Time
Distance = 20 m/s × 25 s = 500 meters

The train travels a distance of 500 meters during the 25 seconds it takes to pass the bridge. Since the train is 100 meters long, the remaining distance must be the length of the bridge.

Length of the bridge = Total distance traveled – Length of the train
Length of the bridge = 500 m – 100 m = 400 meters

Therefore, the length of the bridge is 400 meters.