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 inequality represents how much time the dehumidifier can run before it becomes full?

Question

A. -2h ≤ 50
B. -2h ≥ 50
C. 2h ≤ 50
D. 2h ≥ 50

Answer 1

To determine the inequality that represents how much time the dehumidifier can run before it becomes full, we start by establishing the relationship between the amount of water removed and time.

The dehumidifier removes 2 quarts of water per hour, and it can hold up to 50 quarts of water. We denote \( h \) as the number of hours the dehumidifier runs. After \( h \) hours, the amount of water removed will be \( 2h \) quarts.

We want to ensure that the total amount of water removed does not exceed the dehumidifier's capacity of 50 quarts. Therefore, we set up the inequality:

\[ 2h \leq 50 \]

This means that the amount of water removed (2h) must be less than or equal to the capacity of the dehumidifier (50 quarts).

Thus, the correct inequality is:

C. 2h ≤ 50