High School

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At a restaurant, you noticed two large fish tanks.

- The first fish tank has 200 L of water and is being filled at a rate of 6 L per minute.
- The second fish tank has 500 L of water and is being drained at a rate of 6 L per minute.

Write an equation that describes after how many minutes, \(m\), the water levels will be the same.

Answer :

Final answer:

The water levels in the two fish tanks will be the same after 25 minutes, by setting up an equation using the rates at which the tanks are being filled and drained.

Explanation:

To find out after how many minutes, m, the water levels in the two fish tanks will be the same, we can set up an equation to reflect the rates at which the tanks are being filled and drained. Given that the first fish tank has 200L of water and is being filled at a rate of 6L per minute, the amount of water after m minutes will be 200L + 6L/m. The second fish tank has 500L of water and is being drained at the same rate of 6L per minute, resulting in 500L - 6L/m after m minutes.

Setting the two expressions equal to each other, we have 200L + 6L/m = 500L - 6L/m. To solve for m, we combine like terms and solve the resulting equation:

  • 200L + 6L/m + 6L/m = 500L
  • 200L + 12L/m = 500L
  • 12L/m = 500L - 200L
  • 12L/m = 300L
  • m = 300L / 12L/m
  • m = 25 minutes

Therefore, the water levels will be the same after 25 minutes.

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