A gear wheel with 9 teeth drives a gear wheel with 27 teeth. If the smaller wheel completes 42 revolutions, how many revolutions does the larger wheel make?

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Multiple Choice

A gear wheel with 9 teeth drives a gear wheel with 27 teeth. If the smaller wheel completes 42 revolutions, how many revolutions does the larger wheel make?

Explanation:
When two gears mesh, the amount of arc length moved by the teeth at the contact is the same for both gears. This creates an inverse relationship between their revolutions and the number of teeth: the driven gear turns by a factor equal to the driver’s teeth divided by the driven gear’s teeth. So the larger gear will turn fewer times than the smaller gear when the smaller drives it. Here, the driver has 9 teeth and the driven gear has 27 teeth. If the driver makes 42 revolutions, the larger gear’s revolutions are (9/27) times 42, which is (1/3) × 42 = 14. So the larger wheel makes 14 revolutions.

When two gears mesh, the amount of arc length moved by the teeth at the contact is the same for both gears. This creates an inverse relationship between their revolutions and the number of teeth: the driven gear turns by a factor equal to the driver’s teeth divided by the driven gear’s teeth. So the larger gear will turn fewer times than the smaller gear when the smaller drives it.

Here, the driver has 9 teeth and the driven gear has 27 teeth. If the driver makes 42 revolutions, the larger gear’s revolutions are (9/27) times 42, which is (1/3) × 42 = 14.

So the larger wheel makes 14 revolutions.

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