If a drive pulley rotates at 120RPM and drives a pulley at 150RPM, what is the diameter of the drive pulley if the driven pulley is 6.4" in diameter?

To determine the diameter of the drive pulley based on the given information, we can use the relationship between the speeds and diameters of two pulleys in a belt drive system. This relationship is expressed through the equation of the pulley system:

[ \text{Diameter of Drive Pulley} \times \text{RPM of Drive Pulley} = \text{Diameter of Driven Pulley} \times \text{RPM of Driven Pulley} ]

In this case, the driven pulley has a diameter of 6.4 inches and rotates at 150 RPM, while the drive pulley rotates at 120 RPM. By rearranging and substituting these values into the formula, we get:

[ \text{Diameter of Drive Pulley} \times 120 = 6.4 \times 150 ]

Calculating the right side:

[ 6.4 \times 150 = 960 ]

Now, the equation becomes:

[ \text{Diameter of Drive Pulley} \times 120 = 960 ]

To find the diameter of the drive pulley, divide both sides by 120:

[ \text{Diameter of Drive Pulley} = \frac{960}{120} = 8 \text{ inches