Let t be the number of minutes that have passed since water started being added to the two pools. The total amount of water in the first pool after t minutes is 707 + 18.25t liters, and the total amount of water in the second pool after t minutes is 43.5t liters. We are looking for the value of t that makes these two quantities equal, which represents the time when the two pools have the same amount of water.
We can set the two quantities equal to each other and solve for t to find the value of t that makes the two pools have the same amount of water:
707 + 18.25t = 43.5t
707 = 25.75t
t = 27.5
Therefore, after 27.5 minutes, the two pools will have the same amount of water.
To find the amount of water that will be in each pool when they have the same amount of water, we can substitute the value of t that we found above into the expressions for the total amount of water in each pool:
First pool: 707 + 18.25 * 27.5 = 707 + 501.875 = 1208.875
Second pool: 43.5 * 27.5 = 1208.875
Therefore, when the two pools have the same amount of water, each pool will have 1208.875 liters of water.