Quandaries and Queries


Subject: ratios

Name: matt

if gear A has 12teeth and Gear B has 16teeth and gear C has 10teeth and gear A turns 40 times how many times will gear C turn



Hi Matt,

Gear A has 12 teeth and 12 notches and gear B has 16 teeth and 16 notches. Suppose that before the gears begin to turn, a tooth from gear A is in a notch in gear B. As the gears turn, watch this place where the two gears are in contact. Gear A turns 40 times and, since 12  40 = 480, 480 teeth from gear A pass this contact point. Hence 480 notches from gear B pass this point. But  480/16 = 30 and hence gear B turns 30 times.

Now apply the same argument to the point of contact of gears B and C.


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