Final answer:
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.