Finding pulley diameter with speed in rpm

[Tambourine Man]

Homework Statement

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In a pulley system, pulley A is moving at 1,500 rpm and has a diameter of 15 in. Three pulleys, B, C, and D, all of different sizes, are attached to a single output axle. Speed and torque output are changed within the system by moving the drive belt between pulleys B, C, and D.

A speed of 2,000 rpm is required when the drive belt is connected to pulley C. What is the diameter of pulley C?

The question is here, how do I find the diameter? I don't know the input or output speeds.

Homework Equations

The Attempt at a Solution

2500/1500

(not sure if this is right)
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[billy_joule]

The question is here, how do I find the diameter? I don't know the input or output speeds.

You sure about that?...

... pulley A is moving at 1,500 rpm...

...A speed of 2,000 rpm is required...

Homework Equations

View attachment 109424

There's no equality so that's not an equation.
You're looking for an equation that relates the diameter of a pair of pulleys with their rotational speed, check your notes and/or textbook. You know both RPM's and one diameter so can solve for the single unknown; the second pulleys diameter.