## Cog Ratios

 Difficulty: Rating: GCSE Marks:

GCSE Text:
A handle is attached to cog A that has 8 teeth. This small cog meshes with a medium size cog B that has 16 teeth, and this medium size cog meshes with a large cog C that has 20 teeth.

a)  Express the number of teeth on cog A to cog B to cog C as a ratio in its simplest form.

The handle is turned once per second.

b)  How many times will cog C rotate per hour?

c)  If an Engineer needs to replace cog C with a different cog that will turn 600  times per hour, how many teeth will the replacement cog need to have?

Suggestions:
This question overlaps nicely with Physics learning and encourages students to employ higher order thinking to apply learning on ratio and circle circumference.  Often much discussion occurs regarding the need for calculators or for diameters, but this could easily appear on a non-calc Higher GCSE paper. Students take 4-5 minutes to answer this question in full.

Teachers could extend the learning by considering:

• If the handle on cog A was turned anticlockwise, which direction does cog C turn? What link is there between the number ‘n’ of the cog in the sequence, and the direction in which it turns?

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