The speed v of a gear varies inversely as the number of teet

The speed (v) of a gear varies inversely as the number of teeth (t). If a gear that has 95 teeth makes 24 revolutions per minute (rpm).

A. Find k

B. How many revolutions per minute will a gear that has 54 teeth make?

Solution

speed (v) of a gear varies inversely as the number of teeth (t)

v proprtional 1/t

Lets take k as constant, we can write: v = k/t

24 = k/95

A. k = 24*95 = 2280

B v = 2280/t = 2280/54 = 42.22 revolutions per minute