Hi Rebecca,

First let's get the time units constant. I'm going to choose seconds. There are 60 seconds in a minute so

The circumference of a circle is 2 π times the radius so if the radius of the circle is r feet then its circumference is

2 πr feet.

The pulley moves 10/3 revolutions in a second so that's 2 πr × 10/3 feet in a second. But you are told that the belt, which runs on the pulley, moves at 30 feet in a second. Thus

30 = 2 πr × 10/3

Solve for r.

Penny