Slow Coach

'Slow Coach' printed from https://nrich.maths.org/

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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	and at the same minutes past each hour until ...	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	and at the same minutes past each hour until ...	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.