Question

1. Two containers are being filled with water. One begins with 10 gallons of water and is filled at a rate of 2.5 gallons per minute. The other begins with 24 gallons and is filed at 2.25 gallons per

minute.

Part A: Write an equation that represents the amount of water w, in gallons, with respect to time t, in minutes, for each container

Part B: Solve the system of equations. Show your work

Part C: How long would it take for both of the containers to have the same amount of water? How much water would be in each container?

Answer 1

The equation for the amount of water in each container with respect to time can be represented as w = 10 + 2.5t and w = 24 + 2.25t. Solving the system of equations, we find that it will take 56 minutes for both containers to have the same amount of water, which is 150 gallons.

Step-by-step explanation:

Part A: To represent the amount of water, w, in gallons, with respect to time, t, in minutes, for the container that begins with 10 gallons of water and is filled at a rate of 2.5 gallons per minute, we can use the equation:

w = 10 + 2.5t

Similarly, for the container that begins with 24 gallons and is filled at a rate of 2.25 gallons per minute, the equation would be:

w = 24 + 2.25t

Part B: To solve the system of equations, we can set the two equations equal to each other and solve for t:

10 + 2.5t = 24 + 2.25t

Subtracting 2.25t from both sides, we get:

0.25t = 14

Dividing both sides by 0.25, we find:

t = 56 minutes

Part C: To find the amount of water in each container after 56 minutes, we can substitute t = 56 into either of the original equations. Let's use the first equation:

w = 10 + 2.5(56)

w = 10 + 140

w = 150 gallons

So, after 56 minutes, both containers will have 150 gallons of water.