A 38 tooth gear at 360 RPM drives a gear at 144 RPM. How many teeth are on the gear that is turning 144 RPM?

To determine the number of teeth on the gear that turns at 144 RPM, we can use the relationship between the speeds and the number of teeth on two meshing gears.

The formula related to the speed and number of teeth on gears can be expressed as:

[ \text{RPM}_1 \times \text{Teeth}_1 = \text{RPM}_2 \times \text{Teeth}_2 ]

In this scenario, we have a gear with 38 teeth turning at 360 RPM, which drives another gear turning at 144 RPM. We can let (T_2) represent the number of teeth on the second gear.

Using the formula, we can rearrange it to solve for (T_2):

[ 360 , \text{RPM} \times 38 , \text{Teeth} = 144 , \text{RPM} \times T_2 ]

Calculating the left side:

[ 13680 = 144 \times T_2 ]

Now, we isolate (T_2):

[ T_2 = \frac{13680}{144} ]

Simplifying gives:

[ T_2 =