Final answer:
The first pool's water volume after x minutes is calculated by V1 = 992 + 16x, and the second pool's by V2 = 48x. Setting these expressions equal and solving for x gives us 31 minutes as the time it would take for both pools to have the same amount of water.
Step-by-step explanation:
The student has asked two questions related to rates of water flow and pool volume. First, we need to write expressions for the two pools being filled and then set up an equation to find when they would have the same amount of water.
Expression for Pool Volumes
First Pool: It starts with 992 liters and water is added at a rate of 16 liters per minute. So, after x minutes, the amount of water in the first pool (V1) would be:
V1 = 992 + 16x
Second Pool: It starts empty and water is added at a rate of 48 liters per minute. So, after x minutes, the amount of water in the second pool (V2) would be:
V2 = 48x
Equation for Equal Water Volumes
To find when both pools have the same amount of water, we set the two expressions equal to each other:
992 + 16x = 48x
Simplifying the equation:
992 = 48x - 16x
992 = 32x
x = 992 / 32
x = 31
Thus, it will take 31 minutes for both pools to have the same amount of water.