Devon is throwing a pool party to kick off the summer. Her pool is empty, so she starts filling it with water from a garden hose. There is a proportional relationship between the time Devon has been filling up the pool (in minute), x, and the volume of water in the pool (in gallons), y. The pool has 26 gallons of water in it after 1 minute. Write the equation for the relationship between *x* and *y*.


y =

Since there is a **proportional relationship** between the time \( x \) (in minutes) and the volume of water \( y \) (in gallons), the equation will be of the form:

\[
y = kx
\]

where \( k \) is the constant of proportionality.

Given that the pool has **26 gallons of water after 1 minute**, we can substitute \( x = 1 \) and \( y = 26 \) into the equation to find \( k \):

\[
26 = k \times 1
\]

Thus, \( k = 26 \).

Therefore, the equation for the relationship between \( x \) and \( y \) is:

\[
y = 26x
\]

This means the pool fills at a rate of 26 gallons per minute.

Do you want further details or have any questions? Here are some related questions to explore:

1. How long will it take to fill the pool if its total capacity is 520 gallons?
2. How much water will be in the pool after 10 minutes?
3. What would the equation look like if the pool filled at 30 gallons per minute?
4. How would the equation change if Devon used two hoses, each with a flow rate of 26 gallons per minute?
5. Can this equation be used if the flow rate varies over time?

**Tip**: Proportional relationships always pass through the origin (0, 0).

Devon is throwing a pool party to kick off the summer. Her pool is empty, so she starts filling it with water from a garden hose. There is a proportional relationship between the time Devon has been filling up the pool (in minute), x, and the volume of water in the pool (in gallons), y. The pool has 26 gallons of water in it after 1 minute. Write the equation for the relationship between x and y.

Learn how to calculate the proportional relationship between time and the volume of water in a pool. This problem demonstrates the relationship using the equation y = 26x, where y is the water volume in gallons and x is the time in minutes. Suitable for students in Grades 6-8.

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