Three relationships are described below: I. The cost of hiring a mover is based on the distance traveled and the total weight of the objects moved. II. The amount of time needed to paint a house decreases as the number of painters increases. III. The income of a worker who gets paid an hourly wage depends on the number of hours worked. What type of variation describes each relationship? I is joint, II is direct, and III is inverse. I is direct, II is inverse, and III is joint. I is joint, II is inverse, and III is direct. I is direct, II is joint, and III is inverse.

## Step1: Identify the type of variation for Relationship I<br />### The cost of hiring a mover depends on both the distance traveled and the weight of the objects moved. Since it depends on two variables, this is a joint variation.<br />## Step2: Identify the type of variation for Relationship II<br />### The amount of time needed to paint a house decreases as the number of painters increases. This describes an inverse relationship because one variable increases while the other decreases.<br />## Step3: Identify the type of variation for Relationship III<br />### The income of a worker who gets paid an hourly wage depends on the number of hours worked. This is a direct variation because the income increases directly with the number of hours worked.