Home Time

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


Alice, Beccy, Craig, David, Ellie and Francis all go to the same school. Usually they catch the bus home, but today they are staying later for hockey club. Alice lives the closest to school, so they walk round there and her mum gives the others a lift home.

The map below shows how the children's houses are connected by road (it is not to scale!). To make things easier, just the first letter of each name has been used.

Image
Home Time


Alice's mum sets off from their house (A) with all the children. She needs to go to each house just once and then back home again. How many different routes are there?

In the end, she took a route like this:

Image
Home Time


The entire journey took $1\frac{1}{2}$ hours and she was travelling at an average speed of $30$ miles per hour.

The total distance from A to D is the same as the total distance from E to A, which is $19$ miles.

It took twice as long to get from B to D as it did from D to E.

A is twice as far from F as it is from B.

The distance between A and B is a third of the distance between C and E.

Using this information can you find out how long each road is on the route taken by Alice's mum?