Slow Coach
How many of this company's coaches travelling in the opposite
direction does the 10 am coach from Alphaton pass before reaching
Betaville?
Problem
A coach company runs a service that connects two towns, Alphaton (A) and Betaville (B), which are $90$ miles apart.


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The timetable below gives details of coaches travelling from A to B:




Coaches going from B to A leave at the same times:  


How many of this company's coaches travelling in the opposite direction does the $10$ am coach from A pass before reaching B?


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Getting Started
Draw a diagram of all the coaches on the road when this one sets
off.
Student Solutions
A maths group from Devonshire Primary School sent us a solution for this problem:
The 10am coach will see the 8.40, 9.00, 9.20, 9.40, 10, 10.20, 10.40, 11, 11.20 coach on its way to Betaville. Therefore it sees 9 coaches. We know this because they are travelling at the same speed and on the same path.
Thank you to you all.
Teachers' Resources
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.