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## 'Wonky Watches' printed from http://nrich.maths.org/

## Wonky Watches

Stuart's watch loses two minutes every hour.

Adam's watch gains one minute every hour.

They both set their watches from the radio at 6:00 a.m. then start their journeys to the airport. When they arrive (at the same time) their watches are $10$ minutes apart.

At what time (the real time) did they arrive at the airport?

### Why do this problem?

This problem consolidates children's understanding of the passage of time and encourages them to work systematically towards a solution. There are many ways of approaching this problem so it would be worth drawing attention to this.

### Possible approach

This problem would make a good challenge activity for the end of a block of work on time. You could begin by posing a few quick questions to make sure the children understand what gaining and losing time means. For example, if I wind up my watch so it shows the correct time at 5pm, but it loses three minutes every hour, what time will it say when the real time is 7pm? 8pm ... etc?

You could present the problem itself orally to the group, perhaps writing up the key pieces of information on the board. Allow pairs or small groups to talk about how they might go about solving the problem without saying much more yourself at this stage. After just a few minutes, encourage learners to share some of their thoughts and then give them more time to work on the problem. Give
each group a large sheet of paper so that they can record what they do and tell them that they will present their work to everyone at the end.

Once the pupils have reached a solution and have presented their results, their pieces of paper could be displayed on the wall.

### Key questions

What time will each watch say after an hour? Two hours ...?

How far apart will the times on the two watches be after an hour? Two hours ...?

### Possible extension

You could challenge some children to make up their own version of the problem according to certain criteria, for example, if the watches were $10$ minutes apart on the hour, what could the amount that they gain/lose be?

### Possible support

Breaking the problem down to an hour at a time might help some learners.