Question 1104694
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Let,
x = number of minutes that have elapsed


The first pool contains 823 liters of water. Water is being added to the first pool at a trate of 35.75 liters per minute. So after x minutes, the first pool will have a total of 35.75*x+823 liters of water
The quantity 35.75*x represents the additional amount of water added after those x minutes go by, which is added on top of the 823 liters already there.


Similarly, the second pool will have a total of 22.5*x+1300 liters since it starts off with 1300 liters and we add on 22.5*x additional liters from the hose.


If we want to know when the two pools are filled with the same amount of water, we set the expressions equal to each other and solve for x
Amount of water for pool 1 = Amount of water for pool 2
35.75*x+823 = 22.5*x+1300
35.75*x+823-823 = 22.5*x+1300-823
35.75*x = 22.5*x+477
35.75*x-22.5*x = 22.5*x+477-22.5*x
13.25*x = 477
13.25*x/13.25 = 477/13.25
x = 36


After 36 minutes, the two pools will have the same amount of water.


Plug x = 36 into either expression to get the amount of water
Amount of water for pool 1 = 35.75*x+823
Amount of water for pool 1 = 35.75*36+823
Amount of water for pool 1 = 1287+823
Amount of water for pool 1 = 2110
OR
Amount of water for pool 2 = 22.5*x+1300
Amount of water for pool 2 = 22.5*36+1300
Amount of water for pool 2 = 810+1300
Amount of water for pool 2 = 2110


Technically you only have to pick one equation, but its good practice to use both to confirm we have the right answer. 

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Now to answer the two questions:
Question 1: <font color=blue>After how many minutes will the two pools have the same amount of water?</font>
Answer 1: <font color=red size=4>36 minutes</font>
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Question 2: <font color=blue>How much water will be in the pool when they have the same amount?</font>
Answer 2: <font color=red size=4>2110 liters</font> (this is the amount for each pool; not the combined from both pools)
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