If a motor pulley has a diameter of 3 inches and runs at 1400 RPMs, what is the RPM of a fan pulley with a diameter of 5 1/4 inches?

To determine the RPM of the fan pulley, we can utilize the relationship between the diameters of the pulleys and their rotational speeds, known as the pulley ratio. This relationship indicates that if one pulley drives another, their speeds are inversely proportional to their diameters.

In this case, the motor pulley has a diameter of 3 inches, and it runs at 1400 RPM. The fan pulley, with a diameter of 5.25 inches, will rotate at a speed that can be calculated using the following formula:

[

\text{RPM of Motor} \times \left(\frac{\text{Diameter of Motor}}{\text{Diameter of Fan}}\right) = \text{RPM of Fan}

]

Substituting the values:

[

1400 \times \left(\frac{3}{5.25}\right)

]

Calculating the fraction:

[

\frac{3}{5.25} = \frac{3 \times 4}{5.25 \times 4} = \frac{12}{21} = \frac{4}{7}

]

Now substituting that back into the formula:

[

1400 \times \frac{4}{7} =