Let’s solve the given problem step by step.
We need to determine the coefficient of [tex]\( t \)[/tex] in the equation [tex]\( 18 + ?t = 24 \)[/tex], where [tex]\( t \)[/tex] represents the number of hours it takes to fill the container from its current water height to its maximum height.
1. Understand the Height Change Required:
- The initial height of water in the container is 18 inches.
- The final height of water in the container is 24 inches.
- To find out the change in height required, we calculate the difference between the final height and the initial height:
[tex]\[
24 - 18 = 6 \text{ inches}
\][/tex]
2. Determine the Rate of Increase in Height:
- The faucet drips at a steady rate, causing the water level to rise by 2 inches every hour.
3. Set Up the Equation:
- We are looking for the number of hours [tex]\( t \)[/tex] needed to increase the water level by the required 6 inches. Since the water level increases by 2 inches per hour, our equation would be:
[tex]\[
18 + 2t = 24
\][/tex]
4. Identify the Coefficient of [tex]\( t \)[/tex]:
- The coefficient of [tex]\( t \)[/tex] in the equation is the rate at which the water height increases per hour, which we know is 2.
Therefore, the coefficient of [tex]\( t \)[/tex] in the equation [tex]\( 18 + ?t = 24 \)[/tex] is 2.
