Question

A cylindrical container has a height of 24 inches. Currently, the container is filled with water to a height of 18 inches. A leaky faucet drips into the container, causing the height of the water in the container to increase by 2 inches per hour. The equation below can be used to find t, the number of hours it would take to fill the container. 18 + ?t = 24 What number should be the coefficient of t?

Answer 1

The coefficient of t should be 2, representing the rate of 2 inches per hour by which the water level increases. So, the equation is 18 + 2t = 24, determining it takes 3 hours to fill the container.

Step-by-step explanation:

The student is presented with a linear equation problem that involves finding the coefficient of t (time) to determine how long it will take for a cylindrical container's water level to rise from 18 inches to 24 inches given a constant rate of increase. Since the water level rises by 2 inches per hour, we can fill in the equation 18 + ?t = 24 with the coefficient representing the rate of water level increase per hour, which is 2. Therefore, the complete equation is 18 + 2t = 24.

To find the number of hours t it would take to fill the container, subtract 18 from both sides of the equation: 2t = 24 - 18 which simplifies to 2t = 6. Dividing both sides by 2 yields t = 3. Thus, t, the number of hours to fill the container, is 3.

Answer 2

Given:
height of cylindrical container = 24 inches
height of water in container = 18 inches
leaky faucet increases water by 2 inches per hour.

18 + ?t = 24

The coefficient of t is 2.

18 + 2t = 24
2t = 24 - 18
2t = 6
2t/2 = 6/2
t = 3

It would take 3 hours to fill the container.

18 + 2t = 24
18 + 2(3) = 24
18 + 6 = 24
24 = 24