A large dehumidifier removes 1.6 pints of water from the air around it per hour. The dehumidifier can hold up to 40 pints of water. Which option number represents the inequality that shows how much time the dehumidifier can run before it becomes full?

1 answer

To solve the problem, we need to create an inequality that represents the time the dehumidifier can run before it reaches its maximum capacity of 40 pints.

Let \( t \) represent the time in hours the dehumidifier runs. Since the dehumidifier removes 1.6 pints of water every hour, the amount of water removed after \( t \) hours is given by \( 1.6t \).

To find the time at which the dehumidifier reaches its maximum capacity, we set up the inequality:

\[ 1.6t < 40 \]

This inequality states that the amount of water removed (which is \( 1.6t \)) must be less than the maximum capacity (which is 40 pints).

Now, if you want to solve this inequality for \( t \):

\[ t < \frac{40}{1.6} \] \[ t < 25 \]

Thus, the dehumidifier can run for less than 25 hours before it becomes full. Therefore, the correct option that represents this situation is:

\[ 1.6t < 40 \]