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In the pulley system below, how fast does pulley D rotate, if pulley A rotates at 100 rpm?

A 12.5 rpm

A larger pulley causes a smaller pulley to rotate faster by the ratio of their diameters. If pulley A rotates at 100 rpm, then pulley B rotates at $7217_w102_h38.png$rpm. Since C is directly connected to B it rotates at the same rate (40 rpm). Finally, pulley D will rotate at $4851_w118_h39.png$rpm