Question
A water tank is being filled at a rate of 2.5 gallons per minute. The tank can hold up to 50 gallons of water. Which option represents the inequality that shows how much time the tank can be filled before it overflows?
Answers
GPT-4o mini
To represent the inequality that shows how much time the tank can be filled before it overflows, we can use the following steps:
1. Let's denote \( t \) as the time in minutes that the tank is being filled.
2. The tank is being filled at a rate of 2.5 gallons per minute, so the total amount of water in the tank after \( t \) minutes would be \( 2.5t \) gallons.
3. The tank has a maximum capacity of 50 gallons.
To prevent the tank from overflowing, the amount of water in the tank must be less than or equal to the maximum capacity:
\[
2.5t \leq 50
\]
This inequality shows how much time \( t \) the tank can be filled before it overflows. You can solve it for \( t \) if needed:
\[
t \leq \frac{50}{2.5}
\]
\[
t \leq 20
\]
Thus, the inequality that represents the situation is \( 2.5t \leq 50 \).
1. Let's denote \( t \) as the time in minutes that the tank is being filled.
2. The tank is being filled at a rate of 2.5 gallons per minute, so the total amount of water in the tank after \( t \) minutes would be \( 2.5t \) gallons.
3. The tank has a maximum capacity of 50 gallons.
To prevent the tank from overflowing, the amount of water in the tank must be less than or equal to the maximum capacity:
\[
2.5t \leq 50
\]
This inequality shows how much time \( t \) the tank can be filled before it overflows. You can solve it for \( t \) if needed:
\[
t \leq \frac{50}{2.5}
\]
\[
t \leq 20
\]
Thus, the inequality that represents the situation is \( 2.5t \leq 50 \).