Answer: a) Write an equation that represents the amount of water in the first pool after t minutes, assuming water is only being added and not removed.
We can use the formula for uniform motion to represent the amount of water in the first pool after t minutes:
amount of water = initial amount + rate * time
The initial amount of water in the first pool is 872 liters. The rate at which water is being added to the first pool is 18.25 liters per minute. Therefore, the equation that represents the amount of water in the first pool after t minutes is:
A(t) = 872 + 18.25t
b) Write an equation that represents the amount of water in the second pool after t minutes, assuming water is only being added and not removed.
Similar to part (a), we can use the formula for uniform motion to represent the amount of water in the second pool after t minutes:
amount of water = initial amount + rate * time
The initial amount of water in the second pool is 0 liters, since it is initially empty. The rate at which water is being added to the second pool is 45.5 liters per minute. Therefore, the equation that represents the amount of water in the second pool after t minutes is:
B(t) = 0 + 45.5t
c) How long will it take until the two pools have the same amount of water?
To find the time when the two pools have the same amount of water, we can set the two equations from parts (a) and (b) equal to each other:
A(t) = B(t)
872 + 18.25t = 45.5t
Subtracting 18.25t from both sides, we get:
872 = 27.25t
Dividing both sides by 27.25, we get:
t ≈ 32 minutes
Therefore, it will take approximately 32 minutes until the two pools have the same amount of water.
Explanation: