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A gear ratio r:s is the ratio of the number of teeth of two ...
SAT-math-test SAT math
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A gear ratio r:s is the ratio of the number of teeth of two connected gears. The ratio of the number of revolutions per minute (rpm) of two gear wheels is s:r. In the diagram below, Gear A is turned by a motor. The turning of Gear A causes Gears B and C to turn as well.

If Gear A is rotated by the motor at a rate of 100 rpm, what is the number of revolutions per minute for Gear C?

A) 50

B) 110

C) 200

D) 1,000

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peter
Asked by peterrep:1.7K
University of Lagos Nigeria
29 May 2020

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peter
Peter answeredrep:1.7K
University of Lagos Nigeria
02 November 2020
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 Since Gear A has 20 teeth and Gear B has 60 teeth, the gear ratio for Gears A and B is 20:60.

Thus the ratio of the number of revolutions per minute (rpm) for the two gears is 60:20, or 3:1.

That is, when Gear A turns at 3 rpm, Gear B turns at 1 rpm.

Similarly, since Gear B has 60 teeth and Gear C has 10 teeth, the gear ratio for Gears B and C is 60:10, and the ratio of the rpms for the two gears is 10:60.

That is, when Gear B turns at 1 rpm, Gear C turns at 6 rpm.

Therefore, if Gear A turns at 100 rpm, then Gear B turns at 100/3 rpm, and Gear C turns at 100/3 x 6 = 200 rpm.

Ans C 

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