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P6 Same time, same distance

Printing machines

Printing machines

One step of the worked solution to Printing machines, drawn in pencil.
7 steps, drawn in pencil

See all 7 steps

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The pattern behind it: Same time, same distance

Two travellers spend the same time, or cover the same distance.

In this one. The head start the faster machine builds up while both are running (6 copies a minute for 70 minutes) is exactly the amount the slower machine still has left to print in its extra 30 minutes — so a difference in rate converts straight into a rate.

the same time for bothfasterslowerthe gap grows by 2 shares per hour

How to spot it

Two travellers set off together or one chases another, with constant speeds and a question about who is ahead, when they meet, or how far apart they are.

Common mistake

Children divide the whole distance by the difference in speed instead of dividing the gap between the travellers, or compare distances covered over different lengths of time.

Try one like it

Standard Aladdin and Jasmine — the magic carpet race Aladdin and Jasmine were having a race on their magic flying carpets. They left the same starting point for the market at 13 00. B…
All 12 with this pattern →

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

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