SOLUTION: The speed v of a gear varies inversely as the number of teeth t. If a gear that has 48 teeth makes 24 revolutions per minute (rpm), how many revolutions per minute will a gear that

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Question 885910: The speed v of a gear varies inversely as the number of teeth t. If a gear that has 48 teeth makes 24 revolutions per minute (rpm), how many revolutions per minute will a gear that has 12 teeth make?

Answer by danarchy(1) About Me  (Show Source):
You can put this solution on YOUR website!
Inverse Variation: y varies inversely as x. As x increases, y decreases. As x decreases, y increases. The product of x and y is always constant.
Equation for Inverse Variation: xy = k
So you take 48 * 24 = k = 1152. Then you take K/t = rpm. so 1152/12 = 96 rpm. So with 12 teeth the gear will make 96 revolutions per minute.