Two pools are being filled with water. To start, the first pool contains 2172 liters of water and the second pool contains 2500 liters of water. Water is being added to the first pool at a rate of 34.5 liters per minute. Water is being added to the second pool at a rate of 24.25 liters per minute.After how many minutes will the two pools have the same amount of water?minutesHow much water will be in each pool when they have the same amount?liters
Question
Two pools are being filled with water. To start, the first pool contains 2172 liters of water and the second pool contains 2500 liters of water. Water is being added to the first pool at a rate of 34.5 liters per minute. Water is being added to the second pool at a rate of 24.25 liters per minute.After how many minutes will the two pools have the same amount of water?minutesHow much water will be in each pool when they have the same amount?liters
Solution
To solve this problem, we need to set up an equation that represents the amount of water in each pool over time.
Let's denote the time in minutes as "t".
The first pool starts with 2172 liters and is being filled at a rate of 34.5 liters per minute. So, the amount of water in the first pool at any given time "t" can be represented as 2172 + 34.5t.
The second pool starts with 2500 liters and is being filled at a rate of 24.25 liters per minute. So, the amount of water in the second pool at any given time "t" can be represented as 2500 + 24.25t.
We want to find the time "t" when the amount of water in both pools is the same, so we set the two equations equal to each other and solve for "t":
2172 + 34.5t = 2500 + 24.25t
Subtract 24.25t from both sides:
10.25t = 328
Divide both sides by 10.25:
t = 328 / 10.25 = 32 minutes
So, the two pools will have the same amount of water after 32 minutes.
To find out how much water will be in each pool when they have the same amount, we can substitute t = 32 into either of the original equations. Let's use the first one:
2172 + 34.5 * 32 = 3276 liters
So, each pool will contain 3276 liters of water after 32 minutes.
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