Question

The speed v of a gear varies inversely as the number of teeth t. If a gear that has 56 teeth makes 24 revolutions per minute (rpm), how many revolutions per minute will a gear that has 14 teeth make?

Answer 1

Okay, here we have this:

Considering the provided information, we are going to calculate the requested value, so we obtain the following:

Let us remember that since it is an inverse relationship, then as you increase the teeth, the revolutions decrease and vice versa, then we have:

And always the product of the two variables is constant, therefore:

56*24=x*14

Let's solve for x:

1344=x*14

x=1344/14

x=96

Finally we obtain that a gear that has 14 teeth will make 96 revolutions per minute.