A large dehumidifier removes 2 quarts of water from the air around it per hour. The dehumidifier can hold up to 50 quarts of water. Which option number represents the inequality that shows how much time the dehumidifier can run before it becomes full?

Answer 1

To find the inequality that represents how much time the dehumidifier can run before it becomes full, we start with the information given:

1. The dehumidifier removes 2 quarts of water per hour.
2. It can hold a maximum of 50 quarts of water.

Let \( t \) represent the number of hours the dehumidifier runs. The total amount of water removed after \( t \) hours will be \( 2t \) quarts.

The dehumidifier will be full (i.e., at its maximum capacity) when the amount of water removed equals 50 quarts. Therefore, we set up the following inequality:

\[ 2t < 50 \]

This means that the dehumidifier can run for less than \( t \) hours to avoid becoming full.

To solve for \( t \), we can divide both sides of the inequality by 2:

\[ t < 25 \]

Thus, the inequality representing how much time the dehumidifier can run before it becomes full is:

\[ t < 25 \]

So, if you have options to choose from, the option that represents this is the one that states \( t < 25 \).