A tank contains 150 gallons of water and fills at a rate of 8 gallons per minute. A second tank contains 600 gallons of water and drains at a rate of 10 gallons per minute. After how many minutes will both tanks have the same amount of water?
To find out when both tanks will have the same amount of water, we need to set up an equation to represent the situation.
Let's assume the number of minutes it takes for both tanks to have the same amount of water is 'x'.
In 'x' minutes, the first tank will have filled 8x gallons of water.
In 'x' minutes, the second tank will have drained 10x gallons of water.
We can now set up an equation using the given information:
150 + 8x = 600 - 10x
To solve this equation, we can proceed as follows:
Add 10x to both sides: 150 + 8x + 10x = 600
Combine like terms: 18x + 150 = 600
Subtract 150 from both sides: 18x = 450
Divide both sides by 18: x = 450 / 18
Simplifying this expression, we find that x = 25.
Therefore, it will take 25 minutes for both tanks to have the same amount of water.