A train 50m long moving on a straight track passes a pole in 5 seconds. Find the speed of the train time it will take to cross a bridge 500m long.

If the train passes the pole in 5 seconds, and the train
is 50 meters long, its speed is 10 meters per second.  You can find that by dividing its
length by the time that it takes to pass a given
point.

From the time that the front of the train reaches
the bridge, it will take 50 seconds (500 meters divided by 10 meters per second) for the
front to cross the bridge.  However, the rest of the train will still be on the
bridge.

It will be 5 more seconds (50 meter train divided
by 10 meters per second) for the rest of the train to get off the
bridge.

Therefore, from the time that the front of the
train reaches the bridge, it will be 55 seconds until the end of the train gets off the
bridge on the other side.