### Times

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

### Ten Green Bottles

Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?

# Slow Coach

## Slow Coach

A coach company runs a service that connects two towns, Alphaton (A) and Betaville (B), which are $90$ miles apart.
The timetable below gives details of coaches travelling from A to B:
 A depart 0600 0620 0640 0700 0720 0740 and at the same minutes past each hour until ... 2100 2120 2140 2200 B arrive 0730 0750 0810 0830 0850 0910 2230 2250 2310 2330
Coaches going from B to A leave at the same times:
 B depart 0600 0620 0640 0700 0720 0740 and at the same minutes past each hour until ... 2100 2120 2140 2200 A arrive 0730 0750 0810 0830 0850 0910 2230 2250 2310 2330
How many of this company's coaches travelling in the opposite direction does the $10$ am coach from A pass before reaching B?

### Why do this problem?

This problem is one to use when relating time and distance and especially when looking at timetables and the $24$ hour clock. Timetables are tricky things and they sometimes need careful thinking to make sense of them. There are many conventions involved in their presentation and learners may need help in finding the meanings in them.

### Key questions

Have you drawn a diagram of the buses on the road from A to B?
How many buses are on the road at $0600$?
How many buses are on the road at $0620$, $0640$, $0700$ and so on?
Do you understand how the $24$ hour clock works?

### Possible extension

Learners could find out bus times from a local timetable and even make up their own problem about them.

### Possible support

Suggest starting by drawing a picture all the coaches on the road at various times.