To determine the inequality that shows how much time the tank can be filled before it overflows, we can start by letting \( t \) represent the time in minutes. Given that the water tank is being filled at a rate of 2.5 gallons per minute, the total amount of water \( W \) in the tank after \( t \) minutes can be expressed as:
\[ W = 2.5t \]
The tank can hold a maximum of 50 gallons, so we want to find the time \( t \) such that the amount of water filled does not exceed the tank's capacity. This gives us the inequality:
\[ 2.5t \leq 50 \]
To solve for \( t \), we can divide both sides of the inequality by 2.5:
\[ t \leq \frac{50}{2.5} \]
Calculating the right side:
\[ \frac{50}{2.5} = 20 \]
So, \( t \leq 20 \), which means the tank can be filled for up to 20 minutes before it overflows.
Now, rewriting the original inequality:
\[ 2.5t \leq 50 \]
is equivalent to:
\[ 25t \leq 500 \]
This can be simplified to:
\[ t \leq 20 \]
Thus, the correct option in the responses would be:
25t ≤ 50 (25t is less than or equal to 50).
1 answer