Pregunta
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A full bathtub drains at a constant rate. The amount of water in the bathtub
changes by gallons in minute. What is the rate, in gallons per minuti
at which the amount of water in the bathtub changes? Show your work.

Ask by Lewis Ingram. in the United States
Jan 31,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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The rate at which the amount of water in the bathtub changes is gallons per minute.

Solución

To find the rate at which the amount of water in the bathtub changes, we need to determine the change in the amount of water per minute.
Given:
  • The amount of water in the bathtub changes by gallons in minute.
Let’s denote the rate of change of water in the bathtub as gallons per minute.
We can set up the equation based on the given information:
Now, we can solve for to find the rate at which the amount of water in the bathtub changes.
Solve the equation by following steps:
  • step0: Solve for :
  • step1: Convert the expressions:
  • step2: Swap the sides:
  • step3: Multiply by the reciprocal:
  • step4: Multiply:

    The rate at which the amount of water in the bathtub changes is gallons per minute.

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Bonus Knowledge

To find the rate at which the amount of water in the bathtub changes, we can set up a simple calculation. The change in the amount of water is gallons, which can be converted into an improper fraction:
Now, we need to find out how much water drains per minute. The change occurs over minute, so we divide the total change by the time:
To divide by a fraction, you multiply by its reciprocal:
Now, we perform the multiplication:
Thus, the rate at which the amount of water in the bathtub changes is gallons per minute.

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