A train 50 m long passes over a bridge 250 m long at a velocity of 30 km/h. How long will it take to completely pass over the bridge?

Step 1: Given data

The length of the train is 50 meters.

The length of the bridge is 250 meters.

The velocity of the train is 30 km/h.

Let t time needed for the train to pass the bridge and s be the distance traveled by train.

Now let's convert the velocity of the train into m/s,

$v=30km/h=\frac{30\times 1000}{3600}=8.333m/s.$

Step 2: Finding the total distance to cross:

Here, the train passes its own length in this case.

Therefore,

$$\begin{gathered} \mathrm{s}=\mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{train}+\mathrm{Length}\mathrm{of}\mathrm{the}\mathrm{bridge}. \\ s=50+250=300. \\ s=300m. \end{gathered}$$

Step 3: Finding the time taken to completely pass over the bridge:

We know that;

$$\begin{gathered} \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Velocity}} \\ t=\frac{300}{8.333}=36 \\ t=36sec. \end{gathered}$$

Hence, the train will pass the bridge after 36 sec.