Chapter 3 - Polynomial and Rational Functions - 3.6 Variation - 3.6 Exercises - Page 389: 35

$90\ revolutions/min$

Step 1. Assume $v\ (revolutions/min)$ is the speed of a pulley. Step 2. Assume $d\ (in)$ is the diameter. Step 3. From the given conditions, we have $v=k/d$ and $150=k/3$, thus $k=450$ Step 4. For $d=5\ (in)$ , we have $v=450/5=90\ revolutions/min$