speed over a bridge
How fast is the train travelling as it goes over the bridge?
Age
11 to 14
Challenge level
Problem
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
Student Solutions
Answer: 60 km/h
Image
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.