A large gear with 405 teeth running at 300 rpm turns a small gear 450 rpm. How many teeth does the small gear have?
A) 180
B) 540
C) 320
D) 267
E) 270

Question

Quizplus · Accepted Answer

The number of teeth on the gears is inversely proportional to their speeds. So, $405 \text{ teeth} \times 300 \text{ rpm} = x \text{ teeth} \times 450 \text{ rpm}$. Solving for $x$ gives $x = \frac{405 \times 300}{450} = 270$ teeth.

A Large Gear with 405 Teeth Running at 300 Rpm