https://file.aiquickdraw.com/mathbot/file/1727359815110s2f5iy9y.jpg

In this problem, we need to determine the relationship between the number of gallons of water \( w \) and the time \( t \) in minutes it takes to fill a cooler with water. We are given the following information:

- It took Priya 5 minutes to fill a cooler with 8 gallons of water.
- The faucet flows at a steady rate.
- \( w \) represents the number of gallons of water in the cooler after \( t \) minutes.

First, let's determine the rate at which water is flowing:

\[
\text{Rate of water flow} = \frac{8 \text{ gallons}}{5 \text{ minutes}} = 1.6 \text{ gallons per minute}.
\]

Now that we know the rate is 1.6 gallons per minute, we can write the relationship between \( w \) and \( t \) as:

\[
w = 1.6t.
\]

This is the equation that represents the number of gallons of water \( w \) in the cooler after \( t \) minutes. Now, let's analyze each of the provided options:

- **Option A: \( w = 1.6t \)** — This is correct, as it represents the relationship directly.
  
- **Option B: \( w = 0.625t \)** — This is incorrect because 0.625 gallons per minute is not the correct rate; the correct rate is 1.6 gallons per minute.

- **Option C: \( t = 1.6w \)** — This is incorrect. The relationship between \( w \) and \( t \) should be \( t = \frac{w}{1.6} \), not \( t = 1.6w \).

- **Option D: \( t = 0.625w \)** — This is correct. Rearranging the equation \( w = 1.6t \), we get \( t = \frac{w}{1.6} \), and \( \frac{1}{1.6} \approx 0.625 \), so \( t = 0.625w \) is valid.

### Final Answer:
The correct options are **A** and **D**.

Would you like further clarification on any step? Also, here are 5 related questions for further exploration:

1. If the faucet's flow rate was doubled, what would the new equation relating \( w \) and \( t \) be?
2. How many minutes would it take to fill 12 gallons of water at the current rate?
3. If Priya used a smaller cooler that held only 4 gallons, how much time would it take to fill it?
4. How would the equation change if the rate of water flow was 2 gallons per minute?
5. Can you derive the unit rate from the information given?

**Tip:** When interpreting word problems, always start by identifying the rate of change and establish a linear relationship accordingly.

It took Priya 5 minutes to fill a cooler with 8 gallons of water from a faucet that was flowing at a steady rate. Let w be the number of gallons of water in the cooler after t minutes.
Which of the following statements represent the relationship between w and t?
A. w = 1.6t
B. w = 0.625t
C. t = 1.6w
D. t = 0.625w

Solve a linear relationship problem where Priya fills a cooler with 8 gallons of water in 5 minutes. Learn how to express the relationship between gallons of water (w) and time (t) with the correct equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation