# speed over a bridge

How fast is the train travelling as it goes over the bridge?

A train that is 100 metres long is travelling at a constant speed. It takes 30 seconds to clear a bridge which is 400 metres long.

What speed is the train travelling at, in kilometres per hour?

*This problem is adapted from the World Mathematics Championships*

**Answer**: 60 km/h

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Total distance travelled to clear the bridge is 500 m (the front of the train ends up 500 m from where it started.)

So the train has travelled 500 m in 30 seconds.

**Working up to km/h using multiplication**

30 seconds : 500 m

1 minute : 500 m$\times$2 = 1 km

1 hour : 1 km$\times$60 = 60 km

**Using division to find the speed**

1 hour = 60 minutes = 60$\times$(2$\times$30 seconds) = 120$\times$(30 seconds).

That means there are 120 30-second intervals in an hour. So in an hour, the train would travel this distance 120 times.

120$\times$500 m = 60 000 m = 60 km.