
Read the description of a proportional relationship.
Darnel wants to fill his water bottle between classes, but the water fountain next to his classroom is frustratingly slow. There is a proportional relationship between the amount of water (in ounces) Darnel puts in his water bottle, x, and how long (in seconds) it takes to get that amount, y.
The equation that models this relationship is y=3x.
How much water does Darnel get in 9 seconds? Write your answer as a whole number or decimal.
 ounces

Given that the relationship between the amount of water \( x \) (in ounces) and the time \( y \) (in seconds) is modeled by the equation:

\[
y = 3x
\]

we need to find how much water Darnel gets in 9 seconds. In this case, \( y = 9 \) seconds. We need to solve for \( x \):

\[
9 = 3x
\]

To find \( x \), divide both sides by 3:

\[
x = \frac{9}{3} = 3 \text{ ounces}
\]

So, Darnel gets **3 ounces** of water in 9 seconds.

Would you like more details or have any questions? 

Here are some related questions:

1. How would the amount of water change if the time was doubled?
2. What is the unit rate of water flow in ounces per second?
3. If Darnel needed 12 ounces of water, how long would it take him?
4. How would the equation change if the water flowed faster?
5. Can you express this proportional relationship in a graph?
6. What if the water bottle had a maximum capacity—how would that affect the time?
7. How long would it take to fill 15 ounces of water?
8. Is the relationship still proportional if the water flow speed varies over time?

**Tip:** In any proportional relationship, the constant of proportionality helps to quickly determine one variable when the other is known.

Explore how to solve a proportional relationship problem involving water filling a bottle. Learn how to calculate the amount of water Darnel gets in 9 seconds using the equation y = 3x. Suitable for Grades 6-8 students learning about proportional relationships in mathematics.

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